Trigonometry Questions and Answers

Jason sees a tall building from across town. He turns 90° and walks 100 yards. Jason then turns to face the building, and the angle between his line of sight and his path is 35° as shown below. Which of the following is the closest to the distance from Jason's original position to the building, in yards?

Graph the function over a two-period interval. Give the period and amplitude. y = 3 cos 2x

What are the domain and range of the cosine function? Domain: All Real Numbers Range: (-1,1) Domain: All Real Numbers Range: [-1,1] Domain: [-1,1] Range: All Real Numbers O Domain: All Real Numbers where ... -, 0, ... Range: [-1,1]

Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given. Student A Step 1: Step 2: cos X sin x Step 5: 1 cos x sin x Step 4: cos²x Step 3: cosx+sin² cos x sin x cos x sinx COS X sinx 11: = cot x + tan x cotx + tan x X cot x + tan x sin² x cos x sin x sin x COS X 11 cotx + tan x Student B Step 6: cot x + tan x = cot x + tan x Step 1: secxcsc x = Step 2: secxcscx = cotx + tanx Step 4: secxcscx = Step 3: secxcsc x = cos x sin x Step 5: secxcsc x = sinx cos x cos²x cosxsin x cos²x+sin² x cos x sin x 1 cos x sinx sin² x cos xsin x (x)(sinx) Step 6: sec x csc X = sec x csc X Part A: Did either student verify the identity properly? Explain why or why not. (10 points) Part B: Name two identities that were used in Student A's verification and the steps they appear in. (5 poin

Why type of symmetry does the cosine function have? Cosine is an odd function, meaning it has rotational symmetry about the origin. Cosine is an even function, meaning it has symmetry with respect to the y axis. Cosine is an odd function, meaning it has symmetry with respect to the y axis. Cosine is an even function, meaning it has rotational symmetry about the origin.

Consider the graph of f(x) = sin(x). a. Describe the graph. b. Can this graph be an example of any other function? Hint (b): c. Explain why f(x) = sin(x) cannot be a polynomial function. Hint (c):

Solve the triangle if possible. a=7 c = 12 B =98.3°

Show that if is an integer multiple of 7, then sin(2x) = 2 sin(x). Hint: Graph the equations y = sin(2x) and y = 2-sin(x) on graphing paper or use Desmos calculator Where are the two equations equal? Use the Desmos calculator below to graph the equations.

Which of the following expressions could not be used to determine the exact value of cos 120°? O cos^2(60°) - sin^2(60°) O2cos^(60°) - 1 O 2sin(60°)cos(60°) O 1 - 2sin^2(60°)

Given sin x=- 15/17 and cos x > 0, what is the exact solution of cos 2x? O161/289 O225/289 O161/289 O225/289

The following problem refers to triangle ABC, find all missing parts. Round degrees to 1 decimal places and sides to the nearest whole number. A = 21.6°, B = 51.4°, a = 130 inches A = B C= a= ___________ inches b= ____________Inches C=______________ inches

For the rotation 435°, find the coterminal angle from 0° 0 < 360°, the quadrant and the reference angle. The coterminal angle is __° of which lies in Quadrant with a reference angle of ____°

Why type of symmetry does the sine function have? Sine is an odd function, meaning it has symmetry with respect to the y axis. Sine is an even function, meaning it has rotational symmetry about the origin. Sine is an even function, meaning it has symmetry with respect to the y axis. Sine is an odd function, meaning it has rotational symmetry about the origin.

cos α =-24/25, α a lies in quadrant II, and sin B = √21, ß lies in quadrant II Find cos (α + β). -48-7√21/125 14-24√21/125 -14+24/21/125 48+7√21/125

What are the domain and range of the sine function? Domain: All Real Numbers Range: (-1,1) Domain: All Real Numbers where x≠..... -π/2,π/2,.... Range: [-1,1] Domain: [-1,1] Range: All Real Numbers Domain: All Real Numbers Range: [-1,1]

A farmer wants to build a new barn between her house and a pasture. She wants the ratio of the distance from the house to the barn and the barn to the pasture to be 7 to 1. She creates a map on a coordinate plane to represent her farm. She draws a point at (-20, 2) to represent her house and a point at (12, −6) to represent the pasture. At what point should she draw the point that represents the barn? Enter the correct answer in the boxes.

Suppose a right triangle contains an angle such that sin(θ) =3/7 Enter the exact values of the trig functions below: cot (θ) = sin (θ) = tan (θ) = cos(θ) = csc (θ) = sec (θ)=

Write the expression cotθ cosθ tanθ cscθ using a single trigonometric function. cos θ sin θ sec θ cot θ

7sin(3x) = 4 for the two smallest positive solutions A and B, with A<B A = B= Give your answers accurate to at least two decimal places.

7π/6 in degrees is _____________ degrees The exact form of tan (7π/6) is ___________

Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians. (Enter your answers as a comma-separated list.) (a) 2π/3 (b) -9π/4

A simple graph G on n vertices (n ≥ 2) is drawn in the plane. Prove that if every edge crosses at most one another edge, then the number of edges in G does not exceed 4n-8.

If the terminal side of angle θ, in standard position, passes through the point (-3, 4), what is the value of sin θ ? (A) -5/4 (B) -3/4 (C) 4/5 (D) 4/3

Use a half angle formula or formula for reducing powers to fill in the blanks in the identity below: (cos(3x))² = _____ + ____ cos(_____ x)

According to a Chinese legend from the Han dynasty (206 B.C.E.-220 C.E.), General Han Xin flew a kite over the palace of his enemy to determine the distance between his troops and the palace. If the general let out 800 meters of string and the kite was flying at a 35° angle of elevation, how far away was the palace from General Han Xin's position?

Find all solutions of the equation. Express the solutions in radians in the form a + 2π, where a is in [0,2π). sin x = -√3 / 2

Find the values of the trigonometric functions of from the information given. tan (θ)=12/5, θ in Quadrant III sin(θ) = cos(θ) = csc(θ) = sec(θ) = cot(θ) =

Simplify cos²xtan²x a. csc²x b. sin²x c. cos(x) d. cos⁴x

State the equation of the rational function if the vertical asymptote is x=5, the horizontal asymptote is y=2, and the x-intercept is -(1/2) a) f(x) = 4x-1/2x-5 b) f(x)=2x+1/2x-10 c) f(x)=2x+1/2/x-5 d) f(x) = 2x+1/x-5

The slope of the tangent to the curve f(x) =2^x at x =1 is approximately (to three decimal places): a) 1 b) 0.347 c) 0.693 d) 1.388

Solve 3 cos²(x) + 5 cos(x) - 2 = 0 for the interval 0≤x≤ 2π a) 1.231 and 5.052 b) 1.231 c) 1.231, 2.356, 2.759 and 5.052 d) 5.052

Since the relationship sin²(x) + cos²(x) = 1 is correct, it stands to reason that sec²(x) + csc²(x) = 1 must also be correct. This statement is: a) True for all values of x b) Never true c) True for the interval 0 ≤ x ≤ 2π d) Not true only for the interval 0 ≤ x ≤ 2π

Which of the following is equivalent to: tan (θ)/cos (θ) a) cos(θ)/cot (θ) b) csc(θ)/sin (θ) c) 1 d) sec (θ)/cot (θ)

Although 330° is a special angle on the unit circle, Amar wanted to determine its coordinates using the sum and difference formulas. Part A: Determine cos 330° using the cosine sum identity. Be sure to include all necessary work. (5 points) Part B: Determine sin 330° using the sine difference identity. Be sure to include all necessary work. (5 points)

Which expression is equivalent to tan(x) + cot(x)? cos x/sec x cos(x) sin(x) 1/sin(x) cos(x) 2 tan(x)

Solve the equation on the interval [0, 2TT). cos x - 2 cos x sin x = 0 π/6,5π/6 π/6,π/2,5π/6,3π/2 π/6,5π/6,2π 0,π/6,5π/6,3π/2

To further justify the Cofunction Thebrem, use your calculator to find a value for the given pair of trigonometric functions. The trigonometric functions are cofunctions of complementary angles. Round each answer to four places past the decimal point. sin 14°, cos 76⁰ sin 14° = cos 76⁰ =

Fill in the blank to correctly complete the sentence. For the polar equation r= 6 sin 40, if 0= 15°, then r = For the polar equation r=6 sin 40, if 0=15°, then r = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Consider the trigonometric equation 2 sin(0) + 3 = 4, where the angle is measured in degrees. One set of solutions is θ= Another unique set of solutions is θ=

Considering only the values of ß for which sin ß tan ß sec ß cot ß is defined, which of the following expressions is equivalent to sin ß tan ß sec ß cot ß? Select the correct answer below: sec ß cot β tan β cot tan β tan ß csc ß sec ß

Use identities to find values of the sine and cosine functions for the angle measure. θ, given that cos2θ= and 90° < θ < 180 sinθ = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) cosθ= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Given: cos (4π/9) cos(2π/9) — sin (4π/9) sin(2π/9) 1. Identify the Trig identity that corresponds with the expression above. 2. Simplify and find the exact value. Show all work. Answers without justification will

A building 29.94 feet tall has a shadow that is 33.11 feet long. Find the angle of elevation of the sun to the nearest hundredth of a degree. The angle of elevation is degrees. (Round to the nearest hundredth as needed.)

From the observation deck of a skyscraper, Meena measures a 45° angle of depression to a ship in the harbor below. If the observation deck is 862 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.

Information about △ABC is given. Determine all remaining information about the triangle. Answers must be accurate to three decimal places. If there are multiple triangles with the given information, determine all of them. If a triangle cannot be solved, explain why not. a) A = 60°2 a = 52 b= 6 b) a = 3, b = 8, c = 50°

Find the cosine of the angle between A and B with respect to the standard inner product on M22 A =[3 3] and B = [4 2] [3 -1] [3 2] Carry out all calculations exactly and round to 4 decimal places the final answer only

The point P(x, y) on the unit circle that corresponds to a real number t is given. Find the value of the indicated trigonometric function at t. (3/4, √7/4) Find sin t. A) 3/4 B) 3√7/7 C) √7/3 D) √7/4

Given sinθ= -5/13 and π<θ<3π/2, what is the exact solution of sin 2θ?

Find the exact value of tan (11π/4) using the unit circle. zero 1 -1 2

Find the exact value of the expression: cos(165°) The final solution needs to be simplified for full credit.