Trigonometry Questions and Answers

A building 56.35 feet tall has a shadow that is 61.66 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.)

Rewrite tan 21° in terms of its cofunction. tan 21° = (Type an exact answer. Simplify your answer. Type any angle measures in degrees.)

Use a calculator to evaluate the expression. sin 88° 24' cos 91° 36' + cos 88° 24' sin 91° 36' sin 88° 24' cos 91° 36' + cos 88° 24' sin 91° 36' = ______

Rewrite cot 63° in terms of its cofunction. cot 63°= __ ° (Type an exact answer. Simplify your answer. Type any angle measures in degrees. Do not include the degree symbol in your answer.)

Suppose that you are headed toward a plateau 25.5 meters high. If the angle of elevation to the top of the plateau is 32.5°, how far are you from the base of the plateau? What is your distance from the base of the plateau? ___ meters (Round to one decimal place as needed.)

Evaluate the expression. sin²210° + cos²210° sin²210° + cos²210° = ______________

Match each angle in Column I with its reference angle in Column II. 45° 88° 42° 30° 32°60° Drag each reference angle above to the corresponding angle below. Answers may be used once, more than once, or not at all. I II 92°. ..... 222° ..... -150° ..... -45° ..... 780° ...... 495° ......

Use a calculator to find a decimal approximation of cos 38° / sin 38° Simplify the expression first. cos 38° / sin 38° ≈ ________________

For what angles 0 between 0° and 360° is cos 0= sin 0 true? The angle 0 in degrees is/are_______ (Use a comma to separate answers as needed. Do not include the degree symbol in your answer.)

Evaluate the expression. cos ² 60° + sec ² 150° - csc ²225° cos ²60° + sec ² 150° - csc²225°=[?] (Simplify your answer, including any radicals. Use integers or fraction)

Complete the table with exact trigonometric function values. Do not use a calculator. θ sin θ cos θ tan θ cot θ sec θ csc θ 60° √3/2 1/2 ? ? 2 2√3/2 θ sin θ cos θ tan θ cot θ sec θ csc θ 60° √3/2 1/2 _____ _____ 2 2√3/2

Find all values of θ if θ is in the interval [0°,360°) and has the given function value. cos θ ≈ 0.4433323 The value(s) of θ is/are _______________

Solve the right triangle using the given information. a = 75.6 yd, b = 40.3 yd c= ___ yd (Simplify your answer. Type an integer or a decimal. Round to the nearest tenth if needed.) A=____ (Simplify your answers. Type integers. Round to the nearest ten minutes if needed.) B= ____ (Simplify your answers. Type integers. Round to the nearest ten minutes if needed.)

Use a calculator to find a decimal approximation for each value. Give as many digits as your calculator displays. Simplify the expression before using the calculator. 1/sec (90°-48°) 1/sec (90°-48°)≈____ (Simplify your answer. Round to eight decimal places as needed.)

Find the exact values of the six trigonometric functions for the following angle.30° sin 30° =

Find a value of α in the interval [0°, 90°] that satisfies the given statement. cot α = 1.5106322 α ≈ ____________

For what angles θ between 0° and 360° is cos θ= sin θ true? The angle θ in degrees is/are _________________

Find a value of α in [0°, 90°] that satisfies the given statement. csc α= 1.1979145 α ≈ ___________

(tan x + cot x)² = tan² x + 1 + cot² x + 1 a) True b) False

When an automobile travels uphill or down hill on a highway, it experiences a force due to gravity. This force in pounds is called grade resistance and is modeled by the following equation, where θ is the grade and W is the weight of the automobile. F = W sin θ A 3340 lb car traveling downhill has a grade resistance of -230 lb. What is the angle of the grade? 0=_____________

The shadow of a vertical tower is 74.0 ft long when the angle of elevation of the sun is 34.0°. Find the height of the tower. The tower is ____ft tall.

Solve the right triangle. O= B= a= (Round to the nearest integer as needed.) m (Round to the nearest integer as needed.) m (Round to the nearest integer as needed.)

Solve the right triangle ABC, with C = 90°. B=69.4°, b= 108 in. A = □ °(Simplify your answer. Type an integer or a decimal. Round to the nearest tenth as needed.) a= □in.(Simplify your answer. Type an integer or a decimal. Round to the nearest tenth as needed.) c=□ in. (Simplify your answer. Type a whole number.)

Find the exact value of the following expression. csc (-480)°

Find a value of θ in the interval [0°,90°] that satisfies the given statement. sin θ =0.68223867 θ ≈ _________°

From a window 29.0 ft above the street, the angle of elevation to the top of the building across the street is 48.0° and the angle of depression to the base of this building is 15.0°. Find the height of the building across the street. The height of the building across the street is ___ ft. (Round to the nearest whole number as needed.)

Find the exact value of the sine function of the given angle. 570 sin 570° =_____

Solve the right triangle ABC, with C = 90°. B = 61.1°, b=116 in. A =___ a=___ C=___

sin² x* cos²x =(1-cos 2x)/2 * (1+cos2x)/2 O True O False

(1+tan x)/(1-tan X)=[1+(sinx/cosx)cosx]/[1-(sinx/cosx)cosx] a)True b)False

Solve the right triangle ABC, where C = 90°. a = 77.7 yd, b = 42.7 yd C=___ A =___ B=____

For each of the following angles, find the radian measure of the angle with the given degree measure (you can enter π as 'pi' in your answers): 320⁰= 320⁰= 330⁰= -380°= -360°=

Find the approximate value of cot θ, given that csc θ = -3.5891420 and θ is in quadrant IV. Rationalize denominators when applicable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. cot θ ≈ _____ (Do not round until the final answer. Then round to seven decimal places as needed.) B. The function is undefined.

(1 cos 2x)(1+ cos2x) = 1²- cos 2x² a) True b)False

(sin x+cos x)/(sec x+csc x)=(sin a+cos x)/[(1/cox)+(1/sinx)] a) True b)False

Identify the quadrant or quadrants for the angles satisfying the following conditions. csc α > 0 and sec α > 0 The angles & satisfying the above conditions are in Quadrant ______. (Type your answer as 1, 2, 3, or 4. Use commas to separate answers if needed.)

Sketch an angle θ in standard position such that θ has the least possible positive measure and the point (5,- 12) is on the terminal side of θ. Then find the exact values of the six trigonometric functions for θ. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. sin θ = _____(Simplify your answer. Type an integer or a fraction.) B. The function is undefined.

11. A sinusoidal function has an amplitude of 4 units, a period of 180°, and a maximum point at (0, 9). a) Represent the function with an equation using the cosine function. b) Create a graph of this function over two cycles. (Make sure to label the y-axis with the correct numbers)

Use a calculator to find a decimal approximation for the following trigonometric function. sin 69°54' sin 69°54' ≈ _____ (Simplify your answer. Type an integer or a decimal. Round to eight decimal places as needed.)

Rewrite sec 22° in terms of its cofunction. sec 22° = (Type an exact answer. Simplify your answer. Type any angle measures in degrees. Do not include the degree symbol in your answer.)

Select the correct choices that complete the sentence below. The value of sin 240° is ________ because 240° is in quadrant _________ The reference angle is _________ and the exact value of sin 240° is _________.

Solve the right triangle ABC, with C = 90°. A=48.4°, c = 22.3 ft B= ____° (Simplify your answer. Type an integer or a decimal. Round to the nearest tenth as needed.) a= ____ ft (Simplify your answer. Type an integer or a decimal. Round to the nearest tenth as needed.) b= ____ ft (Simplify your answer. Type an integer or a decimal. Round to the nearest tenth as needed.)

Find the exact value of sin 60°. sin 60° = _____ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

A fan of trigonometry is building a right triangular pool in his backyard. The hypotenuse of the right triangle is 30 feet long and the height of the right triangle is 24 feet long. If the fan of trigonometry wants to purchase a pool cover, how many square feet of material should he purchase?

The terminal side of an angle θ in standard position passes through the point (-3,-6). Use the figure to find the following value. cos θ cos θ = ____ (Type an exact answer in simplified form. Rationalize all denominators.)

Two ships leave a harbor entrance at the same time. The first ship is traveling at a constant 12 miles per hour, while the second is traveling at a constant 14 miles per hour. If the angle between their courses is 146°, how far apart are they after 30 minutes? (Round your answer to the nearest whole number.) __________________ mi

Use the circle shown in the rectangular coordinate system to find two angles, in radians, between - 2π and 2π such that each angle's terminal side passes through the origin and the point indicated on the circle. The two angles that determine the indicated point on the circle are _____

Convert 110° to radians and express your answer in terms of π. 11π/36 19π/9 198π 11π/18

Two planes leave an airport at the same time. Their speeds are 90 miles per hour and 110 miles per hour, and the angle between their courses is 24°. How far apart are they after 1.5 hours? (Round your answer to the nearest whole number.) ________mi

A vector is described. Express the vector in terms of i and j. A plane flying downward toward a runway at 150 miles per hour makes an angle of 4° with the runway.