Trigonometry Questions and Answers

If construction costs are $156,000 per kilometer, find the cost of building the new road in the figure shown to the right.

Sketch the angle and write the sec and tan of the angle if the terminal side of the angle passes through (3, -6). Express each answer as a decimal rounded to the nearest hundredth. Be sure to type your answers to all parts in the answer box. Be sure to show all work on loose leaf as a file upload question at the end.

The following problem refers to triangle ABC. Solve it. Round your degrees and minutes to the nearest whole number. Round the sides to the 3 decimal places. b = 0.75, c = 0.507, A = 46°20'

Given oblique triangle ABC, side a = 12 ft., side b = 17 ft., side c = 10 ft., find the degree of the smallest angle (round to the nearest whole degree). DO NOT FIND ALL THREE ANGLES AND THEN CHOOSE THE MALLEST. Remember that the smallest angles is across from the smallest side. Be sure to type your answers to all parts in the answer box. Be sure to show all work on loose leaf as a file upload question at the end. This question is worth 8 points total. 1 for the answer and 7 for the work.

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?

A ramp is set up from a truck's trunk to the ground. The ramp's end at the edge of the trunk is 3.5 ft high. If the angle between the ramp and the ground is 13 degrees, find the length of the ramp.

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠B₁ is larger than ∠B₂.). a = 38, c = 42, ∠A = 33 ∠B₁ = ∠B₂ = ∠C₁ = ∠C₂ = b₁ = b₂ =

Which of the following real-world scenarios can be modeled using sine or cosine? A teenager's temperature over the course of a school week. The distance from the ground of the air valve of a bicycle tire as a person rides the bike. The height of a tree growing in the forest over the course of a year. The balance of a car loan as each monthly payment is made.

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 exact value, if possible, without a calculator. If it is not possible, use a calculator round to 3 decimal places. #34 sin (tan-¹(4/3))= a) Let θ = tan-¹(4/3) that means: tan(θ)= b) Using refrence triangle to find sin(θ) =

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

Solve 3 sin(x) = cos(x) in radians, to two decimal places for 0≤x≤ π a) 0 b) 0.32 and 3.46 c) There is no solution to this equation for the given interval d) 0.32

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)

The adjacent side of an unknown angle in a right triangle is half as long as the hypotenuse. What is the measure of this unknown angle? a) There is not enough information given to find the angle b) π/6 c) π/2 d) π/3

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 =

Find the exact value of each of the remaining trigonometric functions of 0. Rationalize denominators when applicable. sinθ= √2/6 given that cos θ<0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. cos θ= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function is undefined.

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=