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.

Convert 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.

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.)

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

Find the exact value of t given cot t =√3/3 & t = [π, 2π] .

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.)

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.)

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.)

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.)

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.)

Find θ to four significant digits for 0≤θ<2x if cos θ = 0.7943.

Rewrite the polar equation r = 5 cos(θ) as a Cartesian equation.

Convert the angle in degrees to radians. Round to two decimal places. 134°

Find 8 to four significant digits for 0≤θ<2x if tan θ= -0.6314.

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)

Solve 8 cos(5x) = 4 for the smallest three positive solutions. X =

Solve 5 cos(2x) = 3 for the smallest three positive solutions. x =

Solve 4 sin(π/4 x )=3 for the four smallest positive solutions

Solve 7 sin(π/5 x) =3 for the four smallest positive solutions

Solve 8 sin(π/6 x)=6 for the four smallest positive solutions

Solve 8 cos(6x) = 2 for the smallest three positive solutions.

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

Find all solutions to cos(6φ) - cos(2φ) = sin(4φ) on 0 <φ< π

If csc(x) = 4, for 90° < x < 180°, then sin (x/2)= cos(x/2)= tan(x/2)=

Write the sum as a product: cos(19.9y) + cos(10.3y)

Write the product as a sum or difference: 10 cos(33r)sin (24r) =

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 =

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)

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)

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.)

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)

Find 0 for 0° ≤0<360°. cot 8 = -0.554 8=

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.

Convert 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

An 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-

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___________

Find cos 285° without using calculator. √ [?] - √[ ]/[ ]

Find 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

If y = cos x, how many periods will there be between-5pi and 9pi?

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=

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?