Trigonometry Questions and Answers

1 In the Overview you met Bud and Travis the dirt bike enthusiasts To determine if they can cross a ravine Bud measures distances and angles using a cactus branch to create two congruent triangles For the measurements to work Bud makes sure that the angle of his line of sight with the top of the pole is the same when he sights parallel to the ravine as when he was sighting across the ravine far edge ravine BU B U B2B pole ZU ZU near edge Bud triangle BU represents Bud when his line of sight travels to the top of the pole labeled L and to a point on the opposite edge of the ravine labeled D B U represents Bud s position after he walks from the pole in the direction parallel with the edge of the ravine B U and BU are both Bud s height In both triangles LP represents the pole Based on the method Bud used justify the reason you know the parts in each pair are congruent A a The two triangles above represent the walk that Bud took The first D feet R b Based on the logical arguments you developed in part a what two triangles can you prove congruent How do you know they are congruent ravine B A by c The image below shows Bud s measurements How do these two triangles help justify Bud s estimation that the ravine is less than 25 feet wide opposite edge B U

Given the angle 3 To which quadrant does belong Write your answer as a numerical value Find the reference angle for IN RADIANS Find the point where intersects the unit circle

3 Ms Carone visited London while on vacation and rode The London Eye Ferris wheel After 15 minutes she hit a maximum height of 136 metres and then a minimum height of 1 metre after 30 minutes a Write a sinusoidal function to model this situation where h is the height in metres above the ground and t represents the time in minutes from when Ms Carone boarded the ride 4 marks

Question 4 Any three distinct complex numbers z1 z2 z3 determine a circle or straight line C Prove that z and Z are inverse relations for C if and only like 3 P Z Z Z2 Z3 P Z Z Z2 Z3

11 For the given expressions 1 Identify quadrant in which angle is located 2 Find reference angle 3 Calculate the exact value b Cos 240 4 f Csc 47 3 a Tan 135 e Cot 5T 4 c Sin 330 g Sec 2 7 3 d Cos 1201

Determine the amplitude period and phase shift of the function Graph the function y sin x x The amplitude is Simplify your answer

Find an equation for the line below 6 8 6 2 64 6 DO 8 8

Match the correct statement concerning Trigonometric functions and angles to the correct answer Cos of an angle Sin of an angle Tan of an angle Pythagorean Theorem Hypotenuse Opposite Opposite Hypotenuse Opposite Adjacent Adjacent Hypotenuse a 2 b 2 c 2

I point Solve for the missing parts of the triangle a 5 b 12 A c a B 90 b A 24 62 c 12 A 13 c 22 62 A 22 62 c 13 A 32 c 13 4 A

To use a calculator to evaluate the trigonometric functions of angles measured in degrees first set your calculator in degree mode Find Cos 28 0 998267 0 8829476 0 07203

Find the value of the following tan sin Give your answer in lowest terms Rationalize the denominator if necessary her that belongs in the green box Estet

What should go in the green box A 1 3 5 13 12 Enter a b c or d a sin b cos c tan d all of the above A Enter

What should go in the green box A 18 17 15 Enter a b c d or e a sin b cos c tan d all of the above A

Name the quadrant in which angle 0 must lie for the following to be true sin 0 0 and tan 0 0 Enter a b c d or e a l b ll c III d IV e All of the above

Use the theoretical probability formula to solve the problem Express the probability as a fraction reduced to lov terms You are dealt one card from a standard 52 card deck Find the probability of being dealt an ace or a 7 OA 13 B WA OC 13 OD 8

4 Find the exact value of each of the following a cos 75 Hint you might rewrite the angle as the sum of two friendlier angle b sin 2tan Hint you will need to use the double angle identity for sine

In rhombus ABCD DB 8 and AC 12 Find DC a 50 b 2 13 c 4 13 d 10 e 8 A D 4 E B

In rhombus QRST TR 6 and QS 10 Find TS a 17 34 b 2 34 C 34 d 8 17 e 12 T V R S

X Find x 45 12 X 45 x Give your answer as a simplified radical

Use the One to One Property to solve the equation for x 2x 9 1

Use the One to One Property to solve the equation for x 3x 2 27

What are the dimensions of a right triangle with an eight inch hypotenuse and an area of 16 square inches Enter the lengths of the sides as a comma separated list 5 657 5 657

3 For the given expression tan a 5 points Identify quadrant in which angle is located b 5 points Find the reference angle in radian form c 5 points Calculate the exact value

Convert the polar equation to rectangular form. θ= π/2

Write the following expression in terms of the first power of cosine: * (5 Points). sin B (3-4 cos 2B + cos 4B) (1-2 cos 23 + cos 4³) (1- cos 43). None of these expressions I don't know.

A parallelogram has sides of lengths 10 and 6, and one angle is 42°. The length of the longer diagonal is:* (5 Points) (36 + 100 – 120 cos 138° ) (36 + 100 – 120 cos 42° ) 6 + 10√120 cos 42° None of these expressions I don't know.

Write the trigonometric form of the complex number. (Let 0 ≤ 0 < 2.T.) -5i Z=

Consider the following. -9i(4 + 4i) (a) Write the trigonometric forms of the complex numbers. (Let 0 ≤ θ < 2π.) -9i = (4 + 4i) = (b) Perform the indicated operation using the trigonometric forms. (Let 0 ≤ θ < 2π.) (c) Perform the indicated operation using the standard forms, and check your result with that of part (b).

Find the quotient. Leave the result in trigonometric form. (Let 0 ≤ 0 < 2л.) 8(cos(60°) + i sin(60°))/72(cos(30°) + i sin(30°))

Consider the following. (6 + 6/)(3-3i) (a) Write the trigonometric forms of the complex numbers. (Let 0 ≤ 0 < 2л.) (6 + 6i) = (3 - 31) = (b) Perform the indicated operation using the trigonometric forms. (Let 0 ≤ 0 < 2.) (c) Perform the indicated operation using the standard forms, and check your result with that of part (b).

Write the trigonometric form of the complex number. (Round your angles to two decimal places. Let 0 ≤ 0 < 2л.) 3√3-i Z=

Write the trigonometric form of the complex number. (Let 0 ≤ 0 < 2.) Z=

Find the angle (in radians) between the vectors. (Round your answer to two decimal places. u = 2i - j v = 10i - 5j

Find an equation whose solution is the smallest value of x, in the interval [0, 2x] using the digits 1 to 9, at most one time each. cos(x) + 0 = 0

The same landscaper in the previous problem is asked to design a larger triangular garden with two sides of length 40.0 and 37.5 feet. She determines that the angle between the two sides must be 350. Calculate the following additional information about the garden. a) The length of the third side b) The size of the other two angles Show all work and round answers to one decimal place.

Determine the following trigonometric values of t using the picture of the unit circle below. Round your answers to three digits. Note that sec(pi+t) should be read as sec(π + t) and cot(pi-t) should be read as cot(π - t). Also, if your answer is 0.52 0.48 you must compute it and enter it as a decimal. That is you would enter 1.083.

A landscaper desgins a garden that is roughly triangular. The angle in the northeast corner is 90°, the north side is 22 feet long, and the diagonal side that connects the northwest and southeast corners is 27 feet long. Calculate the triangle's values below and round all answers to two decimal places. Angle in the southest corner = Length of east side =

Which of the following is the result when you divide 3(cos 60° + i sin 60°) by 2(cos 30° + i sin 30°)? a 1.5 b -3 C -1.5 d 3

Suppose you want to use a Half-Angle Identity to find the exact value of the following expression. cos 67.5° A.cos 67.5° =√1 + cos___/2 B.cos 67.5° =-√1 + cos___/2 C.cos 67.5° =-√1 + cos___/2 D.cos 67.5° =√1 + cos___/2

Jeriel leans a 26-foot ladder against a wall so that it forms an angle of 61 with the ground. What's the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest hundredth of a foot if necessary.

The graph of a sine function has an amplitude of 2, a midline of y = 10, and a period of 4. There is no phase shift. The graph is reflected over the x-axis. What is the equation of the function? f(x) = -2 sin (πx/2) +2 f(x) = -4 sin (2x) + 2 f(x) =-2 sin (2πx) + 10 f(x) =-2 sin (πx/2) + 10

A 45-foot ladder is set against the side of a house so that it reaches a window 27 feet up. Find how far the base of the ladder is from the side of the house. Round to the nearest tenth c foot if necessary.

Suppose tan x =7/10 and x is the angle in quadrant 3. Then sin x = cos x =

To evaluate the integral ∫sin³θ cos⁶θ dθ by trigonometric transformation, we use the identity: (A) cos²θ = 1 + cos2θ / 2 (B) sin²θ = 1 - cos2θ / 2 (C) sinθ cosθ = sin2θ / 2 (D) sin²θ = 1 - cos²θ

To determine the value of tan(7π/8) ,which identity could be used? I.(1 - cos(7π/4))/sin(7π/4) II.sin(7π/4)/(1 - cos(7π/4)) III.-{(1 - cos(7π/4))/(1 + cos(7π/4))}^(1/2) a)l only b)I and II only

Suppose is an angle such that cos(θ) =-1/7 a)If 2π <θ<3π, then cos(θ/2)=___ and sin(θ/2)=___

Find the points on the curve y=cos²x/(x+sin x) at which the tangent is: a). Horizontal b). Vertical

Given that tanθ=1/2 and sinθ< 0, find the exact value of each of the remaining five trigonometric functions of θ .

Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers to four decimal places. If an answer does not exist, enter DNE.) lim tan x/tan 9x X→0 x -0.1 -0.01 -0.001 0.001 0.01 0.1 f(x) lim tan x/tan 9x= X→0

Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) lim (5/sin x) x →0+