Trigonometry Questions and Answers
![Find a value of a in [0°, 90°] thatsatisfies the given statement.
sec α= 1.3729405
a=
(Simplify your answer. Type an integer or a decimal. Round to six decimal places as needed.](https://media.kunduz.com/media/sug-question/raw/84171944-1657091557.1255078.jpeg?w=256)
Math - Others
TrigonometryFind a value of a in [0°, 90°] thatsatisfies the given statement.
sec α= 1.3729405
a=
(Simplify your answer. Type an integer or a decimal. Round to six decimal places as needed.
![Convert the following angle to decimal degree notation.
-19° 6'
-19° 6'=
(Round to two decimal places as needed.)](https://media.kunduz.com/media/sug-question/raw/84171753-1657091246.2383337.jpeg?w=256)
Math - Others
TrigonometryConvert the following angle to decimal degree notation.
-19° 6'
-19° 6'=
(Round to two decimal places as needed.)
![Find the exact value of tan 8, given that sin θ = 1/2 and θ is in quadrant II. Rationalize denominators when applicable.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. tan θ=
(Simplify your answer. Type an exact answer, using radicals as needed. Type an integer or a fraction.)
OB. The function is undefined.](https://media.kunduz.com/media/sug-question/raw/84171891-1657091145.069849.jpeg?w=256)
Math - Others
TrigonometryFind the exact value of tan 8, given that sin θ = 1/2 and θ is in quadrant II. Rationalize denominators when applicable.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. tan θ=
(Simplify your answer. Type an exact answer, using radicals as needed. Type an integer or a fraction.)
OB. The function is undefined.
![Find all values of 0 in the interval [0°,360°) that have the given function value.
Cos θ=√2/2
θ=
(Type an integer or a decimal. Use a comma to separate answers as needed.)](https://media.kunduz.com/media/sug-question/raw/84171923-1657091063.1455095.jpeg?w=256)
Math - Others
TrigonometryFind all values of 0 in the interval [0°,360°) that have the given function value.
Cos θ=√2/2
θ=
(Type an integer or a decimal. Use a comma to separate answers as needed.)
![Find the value of the trigonometric function. Round off the result according the provided table.
cos 22.07
cos 22.07⁰ =
Measurements of Accuracy of
angle to Nearest trigonometric function
1° 2 significant digits
0.1 3 significant digits
0.01 4 significant digits](https://media.kunduz.com/media/sug-question/raw/84183974-1657089013.0199232.jpeg?w=256)
Math - Others
TrigonometryFind the value of the trigonometric function. Round off the result according the provided table.
cos 22.07
cos 22.07⁰ =
Measurements of Accuracy of
angle to Nearest trigonometric function
1° 2 significant digits
0.1 3 significant digits
0.01 4 significant digits
![Find the exact value of t given cot t =√3/3 & t = [π, 2π] .](https://media.kunduz.com/media/sug-question/raw/84171148-1657088762.909084.jpeg?w=256)
![Find the values of the trigonometric functions of the angle (in standard position) whose terminal side passes through (-2.-√2)
sin a =
(Simplify your answer. Type an exact answer, using radicals as needed. Use integårs or fractions for any numbers in the expression.)
cos a =
(Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)](https://media.kunduz.com/media/sug-question/raw/84184112-1657088472.7979708.jpeg?w=256)
Math - Others
TrigonometryFind the values of the trigonometric functions of the angle (in standard position) whose terminal side passes through (-2.-√2)
sin a =
(Simplify your answer. Type an exact answer, using radicals as needed. Use integårs or fractions for any numbers in the expression.)
cos a =
(Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)
![Assume that 8 is an angle in standard position whose terminal side contains the point
(-8,15). Find the exact values of the following functions.
sin θ=
(Simplify your answer. Type an integer or a fraction.)
cosθ=
(Simplify your answer. Type an integer or a fraction.)
tan θ =
(Simplify your answer. Type an integer or a fraction.)](https://media.kunduz.com/media/sug-question/raw/84206375-1657041962.316296.jpeg?w=256)
Math - Others
TrigonometryAssume that 8 is an angle in standard position whose terminal side contains the point
(-8,15). Find the exact values of the following functions.
sin θ=
(Simplify your answer. Type an integer or a fraction.)
cosθ=
(Simplify your answer. Type an integer or a fraction.)
tan θ =
(Simplify your answer. Type an integer or a fraction.)
![Assume that is an angle in standard position whose terminal side contains the point
(5.-12). Find the exact values of the following functions.
sin θ=
(Simplify your answer. Type an integer or a fraction,)
cos θ=
(Simplify your answer. Type an integer or a fraction.)](https://media.kunduz.com/media/sug-question/raw/84206126-1657041903.3159878.jpeg?w=256)
Math - Others
TrigonometryAssume that is an angle in standard position whose terminal side contains the point
(5.-12). Find the exact values of the following functions.
sin θ=
(Simplify your answer. Type an integer or a fraction,)
cos θ=
(Simplify your answer. Type an integer or a fraction.)
![Express the given trigonometric functions in terms of the same function of a positive acute angle.
sin 140°, cos 220°
sin 140°
(Type an exact answer.)](https://media.kunduz.com/media/sug-question/raw/84206421-1657041802.077527.jpeg?w=256)
Math - Others
TrigonometryExpress the given trigonometric functions in terms of the same function of a positive acute angle.
sin 140°, cos 220°
sin 140°
(Type an exact answer.)
![Find the value of the given trigonometric function directly from a calculator.
sin 308.65°
sin 308.65° =
(Round to three decimal places as needed.)](https://media.kunduz.com/media/sug-question/raw/84206456-1657041765.571133.jpeg?w=256)
Math - Others
TrigonometryFind the value of the given trigonometric function directly from a calculator.
sin 308.65°
sin 308.65° =
(Round to three decimal places as needed.)
![Find θ to four significant digits for 0≤θ<2x if cos θ = 0.7943.](https://media.kunduz.com/media/sug-question/raw/84207935-1657041347.176747.jpeg?w=256)
![Rewrite the polar equation r = 5 cos(θ) as a Cartesian equation.](https://media.kunduz.com/media/sug-question/raw/84225413-1657041289.8221984.jpeg?w=256)
![Convert the angle in degrees to radians. Round to two decimal places.
134°](https://media.kunduz.com/media/sug-question/raw/84207898-1657041258.9493215.jpeg?w=256)
![Find 8 to four significant digits for 0≤θ<2x if tan θ= -0.6314.](https://media.kunduz.com/media/sug-question/raw/84207925-1657041131.0303273.jpeg?w=256)
![Convert the Cartesian coordinate (6,-2) to polar coordinates, 0 ≤ θ< 2π
r=
Enter exact value.
θ=
(in radian, round to at least one decimal place)](https://media.kunduz.com/media/sug-question/raw/84226828-1657040805.761318.jpeg?w=256)
Math - Others
TrigonometryConvert the Cartesian coordinate (6,-2) to polar coordinates, 0 ≤ θ< 2π
r=
Enter exact value.
θ=
(in radian, round to at least one decimal place)
![Solve 8 cos(5x) = 4 for the smallest three positive solutions.
X =](https://media.kunduz.com/media/sug-question/raw/84227953-1657040521.8685517.jpeg?w=256)
![Solve 5 cos(2x) = 3 for the smallest three positive solutions.
x =](https://media.kunduz.com/media/sug-question/raw/84227941-1657040493.8393734.jpeg?w=256)
![Solve 4 sin(π/4 x )=3 for the four smallest positive solutions](https://media.kunduz.com/media/sug-question/raw/84227969-1657040466.4796193.jpeg?w=256)
![Solve 7 sin(π/5 x) =3 for the four smallest positive solutions](https://media.kunduz.com/media/sug-question/raw/84227978-1657040420.100198.jpeg?w=256)
![Solve 8 sin(π/6 x)=6 for the four smallest positive solutions](https://media.kunduz.com/media/sug-question/raw/84227974-1657040338.799066.jpeg?w=256)
![Solve 8 cos(6x) = 2 for the smallest three positive solutions.](https://media.kunduz.com/media/sug-question/raw/84227946-1657040282.2299433.jpeg?w=256)
![Solve cos(x) = -0.57 on 0 < x < 2pi
There are two solutions, A and B, with A < B
A =
B =
Give your answers accurate to 3 decimal places](https://media.kunduz.com/media/sug-question/raw/84228235-1657040257.0227706.jpeg?w=256)
Math - Others
TrigonometrySolve cos(x) = -0.57 on 0 < x < 2pi
There are two solutions, A and B, with A < B
A =
B =
Give your answers accurate to 3 decimal places
![Find all solutions to cos(6φ) - cos(2φ) = sin(4φ) on 0 <φ< π](https://media.kunduz.com/media/sug-question/raw/84230257-1657039886.219517.jpeg?w=256)
![If csc(x) = 4, for 90° < x < 180°, then
sin (x/2)=
cos(x/2)=
tan(x/2)=](https://media.kunduz.com/media/sug-question/raw/84230272-1657039614.7328405.jpeg?w=256)
![Write the sum as a product:
cos(19.9y) + cos(10.3y)](https://media.kunduz.com/media/sug-question/raw/84228817-1657035200.2440119.jpeg?w=256)
![Write the product as a sum or difference:
10 cos(33r)sin (24r)
=](https://media.kunduz.com/media/sug-question/raw/84229048-1657035037.5058057.jpeg?w=256)
![A curve with polar equation r =44/(9 sin θ+ 73 cos θ)
represents a line. This line has a Cartesian equation of the form y = mx + b,where m and bare
constants. Give the formula for y in terms of x. For example, if the line had equation y = 2x + 3 then
the answer would be 2 x + 3.
y =](https://media.kunduz.com/media/sug-question/raw/84225666-1657029307.738073.jpeg?w=256)
Math - Others
TrigonometryA curve with polar equation r =44/(9 sin θ+ 73 cos θ)
represents a line. This line has a Cartesian equation of the form y = mx + b,where m and bare
constants. Give the formula for y in terms of x. For example, if the line had equation y = 2x + 3 then
the answer would be 2 x + 3.
y =
![Convert the Cartesian coordinate (5,-6) to polar coordinates, 0 ≤ θ < 2π
r =
Enter exact value.
θ=
(in radian, round to at least one decimal place)](https://media.kunduz.com/media/sug-question/raw/84225406-1657029230.1499476.jpeg?w=256)
Math - Others
TrigonometryConvert the Cartesian coordinate (5,-6) to polar coordinates, 0 ≤ θ < 2π
r =
Enter exact value.
θ=
(in radian, round to at least one decimal place)
![Convert the Cartesian coordinate (4,3) to polar coordinates, 0≤ θ < 2π
r =
Enter exact value.
θ =
(in radian, round to at least one decimal place)](https://media.kunduz.com/media/sug-question/raw/84225541-1657029120.2231326.jpeg?w=256)
Math - Others
TrigonometryConvert the Cartesian coordinate (4,3) to polar coordinates, 0≤ θ < 2π
r =
Enter exact value.
θ =
(in radian, round to at least one decimal place)
![Use a sum or difference formula to find the exact value of the trigonometric function.
sin 165°
Rewrite the given trigonometric function using an appropriate sum or difference formula for the sine function. Choose the correct answer below.
OA. sin 165°=cos 120° cos 45°- sin 120° sin 45°
B. sin 165=cos 120° cos 45°+ sin 120° sin45°
OC. sin 165=sin 120° cos 45°+ cos 120° sin 45°
OD. sin 165° = sin 120° cos 45°- cos 120° sin 45"
Find the exact value of sin 165°.
sin 165⁰ -
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)](https://media.kunduz.com/media/sug-question/raw/84211463-1657018868.1693358.jpeg?w=256)
Math - Others
TrigonometryUse a sum or difference formula to find the exact value of the trigonometric function.
sin 165°
Rewrite the given trigonometric function using an appropriate sum or difference formula for the sine function. Choose the correct answer below.
OA. sin 165°=cos 120° cos 45°- sin 120° sin 45°
B. sin 165=cos 120° cos 45°+ sin 120° sin45°
OC. sin 165=sin 120° cos 45°+ cos 120° sin 45°
OD. sin 165° = sin 120° cos 45°- cos 120° sin 45"
Find the exact value of sin 165°.
sin 165⁰ -
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
![Describe in proper order the five transformations required to change the graph of y = cscx into the graph of y = 98 - 12 csc (3 pi /4 x + 9 pi/10)](https://media.kunduz.com/media/sug-question/raw/84211693-1657018667.6643143.jpeg?w=256)
Math - Others
TrigonometryDescribe in proper order the five transformations required to change the graph of y = cscx into the graph of y = 98 - 12 csc (3 pi /4 x + 9 pi/10)
![Find 0 for 0° ≤0<360°.
cot 8 = -0.554
8=](https://media.kunduz.com/media/sug-question/raw/84222551-1657016611.6233456.jpeg?w=256)
![Using the Law of Sines to find a triangle with one obtuse angle if ZA = 47°, a = = 33, b = 35.
If no answer exists, enter DNE for all answers. Otherwise round to at least one decimal place.
LB is degrees;
LC is degrees;
C=
Assume LA is opposite side a, ZB is opposite side b, and ZC is opposite side c.](https://media.kunduz.com/media/sug-question/raw/84213471-1657015677.3579159.jpeg?w=256)
Math - Others
TrigonometryUsing the Law of Sines to find a triangle with one obtuse angle if ZA = 47°, a = = 33, b = 35.
If no answer exists, enter DNE for all answers. Otherwise round to at least one decimal place.
LB is degrees;
LC is degrees;
C=
Assume LA is opposite side a, ZB is opposite side b, and ZC is opposite side c.
![Convert the angle in degrees to radians. Express your answer as a multiple of π
55°](https://media.kunduz.com/media/sug-question/raw/84207847-1657015575.726079.jpeg?w=256)
Math - Others
TrigonometryConvert the angle in degrees to radians. Express your answer as a multiple of π
55°
![Use Identities to find the exact value. cos7π/ 12 cos 5π/12 + sin 7π/12 sin 5π/12](https://media.kunduz.com/media/sug-question/raw/84208745-1657015229.4610054.jpeg?w=256)
Math - Others
TrigonometryUse Identities to find the exact value. cos7π/ 12 cos 5π/12 + sin 7π/12 sin 5π/12
![An angle passes through the point (11, 2). What is the compass heading of this angle?](https://media.kunduz.com/media/sug-question/raw/84226328-1657014833.7490306.jpeg?w=256)
Math - Others
TrigonometryAn angle passes through the point (11, 2). What is the compass heading of this angle?
![Consider g(w) w²-2w-13 on [ - 5,3].
Determine the interval over which g is continuous and the interval over which g is differentiable
g is continuous on-
g is differentiable on-](https://media.kunduz.com/media/sug-question/raw/84229580-1656998883.6495433.jpeg?w=256)
Math - Others
TrigonometryConsider g(w) w²-2w-13 on [ - 5,3].
Determine the interval over which g is continuous and the interval over which g is differentiable
g is continuous on-
g is differentiable on-
![Consider f(u) = - 10(u - 9)² + 10(u - 9)^4+ 13 on [8, 10].
Determine the interval over which f is continuous and the interval over which f is differentiable.
f is continuous on_________
f is differentiable on___________](https://media.kunduz.com/media/sug-question/raw/84229581-1656998812.8258688.jpeg?w=256)
Math - Others
TrigonometryConsider f(u) = - 10(u - 9)² + 10(u - 9)^4+ 13 on [8, 10].
Determine the interval over which f is continuous and the interval over which f is differentiable.
f is continuous on_________
f is differentiable on___________
![Find cos 285° without using calculator.
√ [?] - √[ ]/[ ]](https://media.kunduz.com/media/sug-question/raw/84229307-1656998651.1778617.jpeg?w=256)
![Find sin 2θ if θ is in the firstquadrant and tan θ = 40./9
sin 2θ = __
Round your answer to the nearest thousandth.](https://media.kunduz.com/media/sug-question/raw/84229382-1656998543.4940875.jpeg?w=256)
Math - Others
TrigonometryFind sin 2θ if θ is in the firstquadrant and tan θ = 40./9
sin 2θ = __
Round your answer to the nearest thousandth.
![Find tan (-15°).
A. -(2+√3)
B. 2-√3
C. √3-2
D. 2+√3](https://media.kunduz.com/media/sug-question/raw/84229341-1656998403.281864.jpeg?w=256)
![If y = cos x, how many periods will there be between-5pi and 9pi?](https://media.kunduz.com/media/sug-question/raw/84227498-1656998286.0871093.jpeg?w=256)
![Assume that 0 is an angle in standard position whose terminal side contains the point
(-8,15). Find the exact values of the following functions.
sin theta=
(Simplify your answer. Type an integer or a fraction.)
cos theta=](https://media.kunduz.com/media/sug-question/raw/84206166-1656958609.2339244.jpeg?w=256)
Math - Others
TrigonometryAssume that 0 is an angle in standard position whose terminal side contains the point
(-8,15). Find the exact values of the following functions.
sin theta=
(Simplify your answer. Type an integer or a fraction.)
cos theta=
![A boat travels 21 miles east from a lighthouse
then changes direction
traveling 22° south of west for 9 miles.
How far is the ship from the
lighthouse?](https://media.kunduz.com/media/sug-question/raw/84201729-1656517473.8956933.jpeg?w=256)
Math - Others
TrigonometryA boat travels 21 miles east from a lighthouse
then changes direction
traveling 22° south of west for 9 miles.
How far is the ship from the
lighthouse?