Trigonometry Questions and Answers
Math
TrigonometryYou are given that cos(A) =5/13 with A in Quadrant III, and cos(B) =8/17 with B in Quadrant I. Find cos(A + B).
Give your answer as a fraction.
Provide your answer below:
cos (A + B))=
Math
TrigonometryFind the exact value of the expression given below.
cos(15)
..…..
cos(15%) =
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)
Math
TrigonometryWrite the function value in terms of the cofunction of a complementary angle.
sin 61°
Math
TrigonometryEvaluate the following expression with a calculator.
arccot (3.5)
Express your answer in degrees, and round to the nearest hundredth.
Hint: Make sure your answer is within the range of the arccot function.
Provide your answer below:
0=
Math
TrigonometryWhich of the following is equivalent to sin(3) tan ß csc ßcot 3 for all values of 3 for which sin(6) tan 6 csc ß cot Bis
defined?
Select the correct answer below:
0 1
O1
O sec B
tan B
Math
TrigonometryWhich of the following is equivalent to csc² β(sec β 1) (sec β + 1) for all values of β for which
csc² β(sec β1) (sec β + 1) is defined?
Select the correct answer below:
sinβcos β
cot²β
sinβ
sec²β
sinβtanβ
Math
TrigonometryFind the exact value of the expression given below.
cos(105)
Rewrite the expression using a sum or difference formula. Choose the correct answer below.
A. cos(105°) = cos (60° +45°) = sin (60°) cos (45°) + cos (60°) sin (45°)
B. cos(105°) = cos (60° +45°) = cos (60°) cos (45°) sin (60°) sin (45°)
C. cos(105%) = cos (60° +45°) = sin (60°) cos (45°)  cos (60°) sin (45°)
D. cos(105) = cos (60° +45°) = cos (60°) cos (45°) + sin (60°) sin (45°)
*****
The exact value of cos(105°) is
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)
Math
TrigonometryFirst, determine the quadrant for θ, then find x, y, and r; and finally, give all six trigonometric ratios for θ given the following information:
tan(θ) = 2/9 and cos(θ) < 0
Math
TrigonometryConsidering only the values of 3 for which the expression is defined, which of the following is equivalent to the expression below?
cos(β).tanβ.csc(β).sec(β)
Math
TrigonometryGiven sin(A) =1/3 with A in quadrant II and cos(B) = 5/9 with B in quadrant III. Solve for sin(A + B), and cos(A + B) and tan(A + B). Leave an exact answer.
sin(A + B) =
cos(A + B)=
tan(A + B)=
Math
TrigonometryDetermine the exact values of sin and cos
given that the terminal side of angle
intersects
4
the unit circle in the first quadrant at (y).
15
Provide your answer below:
sin = 0
50=
=
COS
Math
TrigonometryVerify that the following equation is an identity.
sin 12a=4 sin 3a cos 3a cos 6a
To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformation and transform the expression at each step.
Math
TrigonometryIf f(x) = 3sin¹x2cos¹x, then f(x) is
(A) even function
(C) neither even nor odd
(B) odd function
(D) even as well as odd function.
Math
TrigonometryConsider the generalized cosine function: f(x) = A cos(B(x  h)) + k.
(a) What is the period of f(x)?
(b) What is the midline of the function f(x)? y =
(c) What is the amplitude of the function f(x).
Math
TrigonometryWhat's a radian?
A) The ratio between a circle's circumference and its radius
B) The ratio between a circle's diameter and its radius
C)
An angle made at the center of a circle by an arc whose length is equal to the
radius of the circle
D) The distance halfway around a circle
Math
TrigonometryFind the mid points between the xintercept and each of the vertical asymptotes of
the function y = 5/2tan(2x)
Math
TrigonometrySolve the following equation on the interval [0°, 360°). Round answers to the nearest tenth. If there is no solution, indicate "No Solution."
 10sin(x) = 4csc(x)  3
Math
TrigonometryUse appropriate Identities to rewrite the following expression in terms containing only first powers of sine.
8tanx
1+tan2x
Math
TrigonometryA 13ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12ft from the house, the base is moving at the rate of 5ft/sec. How fast is the top of the ladder sliding down the wall then?
Math
TrigonometryConsider the function y =  4 cos (2x). In the "Show Work" area:
(a) Determine the amplitude and period.
(b) Identify the 5 key points of the first cycle.
(c) Then, sketch the graph of the function showing at least two full cycles.
Math
TrigonometryA customer brings a special window frame, shown in the following diagram, to a glass shop. The wood frame has inside dimensions FG = 80 cm and HF = 136 cm. Calculate the length of the arc HI, if the centre of the circle of the arc is the midpoint of FG.
Math
TrigonometryAnalyze and sketch a graph of the function. Identify any relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.
f(x) = arcsec(2x)
maximum (x, y) =
minimum (x, y) =
horizontal asymptote y =
Math
TrigonometryF
video
nswer:
(Diagram is not to scale.)
Edulastic: Formati... Classes
Olivia is 1.25 meters tall. At 3 p.m., she measures the length of a tree's shadow to be
32.25 meters. She stands 28.1 meters away from the tree, so that the tip of her
shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
32.25 m
q
1.25 m
28.1 m
DeltaMath
m Submit Answer
Unit 1 Home  Hu...
San Dimas H
Math
TrigonometryFind the radian measure of the arc of a sector that has a sector area of
72π and the area of the circle is 360л. Leave your answer in terms of .
072
2π/5
75°
1.256
Math
TrigonometryVerify that the equation is an identity.
tan²a + 1/(sec α)= sec α
To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression
at each step.
tan ²x + 1/(sec a)= /seca
Apply a Pythagorean identity.
Apply an evenodd identity.
Apply a quotient identity.
Math
Trigonometry(1) Rewrite the trigonometric function in terms of reference angle (do not evaluate):
(³3)0
cot
(2) Using the above, evaluate the exact value of the trigonometric function:
cot
ot (²3)=0
Note: Decimals are NOT allowed in the answers.
Math
TrigonometryDetermine the exact value of two trig functions of a given angle (one in degrees and one in radians) by drawing a picture of each given angle in standard position, finding each reference angle, and then determining each requested trig value.
Math
TrigonometryHenry is riding a Ferris wheel at a carnival. After a time t, his height H above the ground is given by the following formula. H=a cos (bt)+c Find Henry's height above the ground when a=30 m, b= rad/s, t = 6 s, and c = 41 m. 2π 11 Do not round any intermediate computations. Round your answer to the nearest hundredth.
Math
TrigonometryProve the identity.
sin²x sin4x= cos²xcos4x
Note that each Statement must be based on a Rule chosen from the Rule menu. To see a deta
select the More Information Button to the right of the Rule.
Math
TrigonometryUse the quadratic formula to solve for x.
2x²8x=1
Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Math
TrigonometryProve the identity.
cot²x (sec²x1)=1
Note that each Statement must be based on a Rule chosen from the Rule menu. the right of the Rule.
Math
TrigonometryIn studies of fluid mechanics, the equation
Y₁V₁ sin(a) = 72V2 sin(a  B),
where 1, 2, V1, V₂ are constants, sometimes arises. Show that if y1 V₁ = 72V2, the equation is equivalent
to cos(3) cot(a) sin(3) = 1.

Math
TrigonometryA rope with a Ingth of 3.5 meters is tied from a stake in the ground to the top of a tent. It forms a 17 degree angle with the ground. How tall is the tent?
Select one:
3.Stan(17)
3.5cos(17)
3.5sin(17)
(sin(17))/3.5
Math
TrigonometryConsider the function y = 5 cos (2x). In the "Show Work" area:
(a) Determine the amplitude and period.
(b) Identify the 5 key points of the first cycle.
(c) Then, sketch the graph of the function showing at least two full cycles.
Math
TrigonometryIn 16, match each statement with the correct value.
Drag each of the values given above into the appropriate area to match the descriptions below.
1. The least positive value k for which x=k is a vertical asymptote for y = sec x
2. The least positive value k for which x = k is a vertical asymptote for y = csc x
3. The least positive value that is in the range of y = secx
4. The greatest negative value that is in the range of y = csc x.
5. The greatest negative value of x for which secx = 1
6. The least positive value of x for which csc x= 1
Math
TrigonometryGraph the curve given below over the given interval, together with its tangents at the given values of x. Label each curve and tangent..
y = sec x,π/2<x<π/2,x=π/3,π/4
What is the equation of the tangent (I) to the curve at x = ?
3
*****
Math
TrigonometryA 20meter line is used to tether a heliumfilled balloon. Because of a breeze, the line makes an angle of approximately 85° with the ground. Use a trigonometric function to write an equation involving the unknown quantity.
Math
TrigonometryA ramp is propped against the back of a truck. There is a 30 degree
angle between the ramp and the horizontal pavement.
If the distance along the ground from the end of the ramp to the point
on the ground below the back of the truck is 13 feet, how long is the
ramp, in feet? Round your answer to the nearest whole number.
Math
TrigonometryWhen working in twopoint geometric perspective, artists must scale their work to fit on the paper or canvas they are using. In doing so the expression A/B arises, where A = tan (θ) and B = cos(θ)sin(θ)/1 cos² (θ) Show that A/B = tan² (θ).
Math
TrigonometryUse a powerreducing identity to rewrite the following expression below in terms containing only first powers of cosine.
cos6(x)
Math
TrigonometryA surveyor needs to determine the distance between two points that lie on opposite banks of a river. Two points, A and C, along one bank are 250 yards apart. The point B is on the opposite bank. Angle A is 64° and angle C is 51°. Find the distance between A and B to the nearest tenth of a yard.
Math
TrigonometryThe Unit Circle gives exact values of trig functions at special angles. When the angle is not one of the special angles, we may sometimes use the Summation Identities and the Even/Odd Identities to evaluate it.
Rewrite the following trig expression using a Summation Identity and special angles of your choice from the Unit Circle. There are many correct ways to do this, but do not yet find the value. (Do not worry about typing the little o degree symbol.)
cos (255°) =
Math
TrigonometryA particular curve is represented parametrically by
x = 5 cos 2t, y = 6 sin 21, t ∈ [0, π/2].
(a) As t increases on [0, π/2], in which direction is the point (x(t), y(t)) moving?
(b) What is the corresponding Cartesian equation for this curve (the equation in x and y only)?
Cartesian equation: = 0.!
(c) Give the smallest and largest values of y taken by this curve
≤ y ≤