Trigonometry Questions and Answers

You 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))=

Find the exact value of the expression given below. COS (π/12)

Find 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.)

Write the function value in terms of the cofunction of a complementary angle. sin 61°

Evaluate 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=

Which 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 O-1 O sec B tan B

Which of the following is equivalent to csc² β(sec β- 1) (sec β + 1) for all values of β for which csc² β(sec β-1) (sec β + 1) is defined? Select the correct answer below: sinβcos β cot²β sinβ sec²β sinβtanβ

Find 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.)

First, 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

Considering 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)

Given 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)=

Determine 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

Verify 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.

If f(x) = 3sin-¹x-2cos-¹x, then f(x) is (A) even function (C) neither even nor odd (B) odd function (D) even as well as odd function.

Venly that the following equation is an identity. sin 12α =4 sin 3α cos 3α cos 6α

Consider 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).

What'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

Find the mid points between the x-intercept and each of the vertical asymptotes of the function y = 5/2tan(2x)

Solve 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

Use appropriate Identities to rewrite the following expression in terms containing only first powers of sine. -8tanx 1+tan2x

A 13-ft 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?

Use trigonometric Identities to simplify the expression. 1/cot(x)tan(-x)

Consider 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.

A 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.

Analyze 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 =

F 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

Find 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

Verify 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 even-odd identity. Apply a quotient identity.

(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 (²-3)=0 Note: Decimals are NOT allowed in the answers.

Determine 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.

Use a cofunction to write an expression equal to csc 72°.

Henry 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.

Prove the identity. sin²x- -sin4x= cos²x-cos4x 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.

Use the quadratic formula to solve for x. 2x²-8x=1 Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas.

Use a cofunction to write an expression equal to tan π/7

Prove the identity. cot²x (sec²x-1)=1 Note that each Statement must be based on a Rule chosen from the Rule menu. the right of the Rule.

In 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. -

If cos(θ)= 1/5 and is in the 4th quadrant, find the exact value for sin (θ)

If θ=5π/6, then sin (θ) = cos(θ) = Give exact values. No decimals allowed!

A 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

Consider 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.

In 1-6, 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

Graph 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 *****

A 20-meter line is used to tether a helium-filled 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.

A 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.

When working in two-point 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).

Use a power-reducing identity to rewrite the following expression below in terms containing only first powers of cosine. cos6(x)

A 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.

The 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°) =

A 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 ≤