Trigonometry Questions and Answers

Use a graphing utility to graph the function and visually estimate the limits. (Round your answers to three decimal place.) f(x) = 7x cos x (a) lim f(x) = x→0 (b) lim f(x) = x→π/3

(a) For each function below, indicate whether it is odd, even, or neither. f(x)= tan x Odd Even Neither g(x)=sin x Odd Even Neither (b) tan (-71°)= (c) sin (-3π/8)=

A gun with a muzzle velocity of 1210 feet per second is fired at an angle of 7° above the horizontal. Find the vertical and horizontal components of the velocity. (Round your answers to one decimal place.) horizontal vertical

Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.) A = 130°, a = b = 15 B = C = c =

Find the area of the triangle. Round your answer to one decimal place. C = 103° 15', a = 18, b = 28

Use the Law of Sines to solve the triangle. Round your answers to two decimal places. A = 94.9°, C = 11.2°, a = 28.6 B = ° b: c=

Given that sin a = 2/7 and cos b =-(1/4) and a and b are in the interval (π/2, π), find sin(a + b) and cos (a - b). Give the exact answers. To enter the square root of a number, type "sqrt(a)". For example, type "sqrt(2)" to enter √2. sin(a + b) = cos (a - b) =

Solve the equation for θ if 0° ≤ θ < 360°. 2 cosθ + 1 = secθ θ=_____

tan(arcsin(-0.16095496)) = ___ Round to 6 decirnal places.

23. A sector of a circle has a central angle of 45°. find the area. of the sector if the radius of the circle is 5cm. cm2

write the product as a sum or difference 6 Sin (35c) Sin(11c)=

13. Solve sin(x) = -0.16 on 0≤x < 2π A= B= Give answers accurate to 3 decimal places.

If tan (θ) = 12/5,0 ≤ θ ≤ π/2, then Sin (θ)= Cos(θ)= Sec(θ)=

if csc (x)=7, for 90°<x< 180°, then sin (x/2) = cos (x/2) = tan (x/2) =

Find all solutions to 2 sin (θ) = √3 on the interval 0 ≤θ < 2π θ= Give answer as exact values, as a list

Suppose a = 5 and b = 6 Find an exact value or give at least two decimal places: sin (A) = cos(A)= tan (A) = sec (A)= csc (A) = cot (A) =

Find a value of 0 in the interval [0°,90°] that satisfies the given statement. tan θ=0.63056645 Find a value of a in [0°, 90°] that satisfies the given statement. cosα =1.1266023

Find the exact values of sin 2u, cos 2u, tan2u if cosu =(-3/7) and π<u<3π/2

Given z = -7 -3i, rewrite z in trigonometric form. 6.325 (cos 23.199° + isin 23.199⁰) 7.616(cos 23.199° + isin 23.199⁰) 6.325(cos 203.199° + isin 203.199⁰) 7.616(cos 203.199° + isin 203.199°)

Convert the polar equation r = 8cos θ to a rectangular.equation.

Suppose that is in standard position and that the terminal side of is in the fourth quadrant and is perpendicular to the line given below. y =14x+6 Compute the following. Keep your answers exact! Decimal approximations may be marked as incorrect. sin(θ) = tan(θ) = sec(θ) =

Find all solutions of the equation. csc θ sin θ= 1 all θ except θ= 2πn for n = 0, +-1, +-2, ... all 8 except θ= πn for n = 0, +-1, +-2,... all θ all θ except θ=0 no solution

A triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the Pythagorean Theorem. What are the measures of the other 2 angles?

Find the exact value of cos π/3 in simplest form with a rational denominator.

Fill in the blank with an appropriate measure. sin (40°) = cos(___°)

In which quadrant does 0 lie if the following statements are true: cos θ< 0 and csc θ > 0 Quadrant I Quadrant III Quadrant II Quadrant IV

Establish the identity cos θ + sin θ /sin θ - cos θ-sin θ /cos θ =sec θ csc θ A. Cancellation Property B. Even-Odd Identity C. Reciprocal Identity D. Pythagorean Identity E. Quotient Identity Subtract the fractions on the left side. Apply the appropriate Pythagorean identity to simplify the numerator (Simplify your answer.) ___/cos sin The fraction from the previous step then simplifies to sec θ csc θ using what?

Sin 43 = (Round answers to the nearest tenth.)

Let sin(θ)=3√27sin(θ)=327. Find all possible values of cos(θ)cos(θ).

Find the exact value of s in the given interval that has the given circular function value. Do not use a calculator. [0,π/2] ; sins=1/2

If 5secθ - 2tanθ = 5, then the value of 5tanθ - 2secθ can be (1) 7 (3) 3 (2) 5 (4) 2

Verify the identity. secx-secx sin²x = cos x 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. secx-secx sin ²x = sec x (Do not simplify.) = sec x (Do not simplify.) = cos x

Verify the following identity. 2 sin ² x + cos2x = 1 To transform the left side into the right side, ___should be changed to___and the left side simplified.

Solve the equation on the interval [0,2π). cos (2θ) =√3/2 What are the solutions to cos (2θ) =√3/2 in the interval [0,2π)? Select the correct choice and fill in any answer boxes in your choice below. A. θ= (Simplify your answer. Type an exact answer, using as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no solution.

Consider the function f(x) = cot(x) a) Sketch two cycles of y-f(x) from (-2π,2π), labeling the all the key points. b) What should the domain of f(x) be restricted to make f(x) one-to-one (and pass the HLT)? NOTE: Answers can vary. c) Based on your answer from part (b), sketch the graph of the inverse function of y=cot(x) and give the domain and range of the inverse function. d) Show how to find cot-¹(-√3) exactly, in exact terms. Include a properly drawn reference angle (as always) for support.

Find the exact value of each expression. (a) cos 75° + cos 15° (b) cos 67.5° cos 22.5°

Solve the right triangle. M= n= p= (Round to one decimal place as needed.) m (Round to the nearest integer as needed.) m (Round to the nearest integer as needed.) .... M n P P 49.4° 126 m N

Use a calculator to evaluate the expression. cos2 (19°) + sin 2 (19°) 2 cos² (19°) + sin ² (19°) = (Simplify your answer.)

A 12.5-m fire truck ladder is leaning against a wall. Find the distance d the ladder goes up the wall (above the fire truck) if the ladder makes an angle of 26° 34' with the horizontal. 12.5 m d 26° 341 d≈ m (Simplify your answer. Type an integer or a decimal. Round to the nearest hundredth.)

Find the exact value of each part labeled with a variable in the following figure. h= 30° C= 63 h C F d n 60° 63√3 2 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expre COLL (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expre

Use Osborn's rule or otherwise to prove that: a) 1 - tanh²x = sech²x b) coth²x - 1 = cosech²x c) cosh²x = 2sinh²x + 1 d) tanh²x = e) cosh²x = f) cothx = 2cosech²x + tanhx

Solve for x in the interval 0 ≤x ≤ 2π 2 sin x + 1= csc X

What is the surface area of the cylinder with height 7 cm and radius 8 cm?

The sines of two angles of a triangle are equal to 5/13 and 99/101. What is the cosine of the third angle? (a) 255/1313 (b) 265/1313 (c) 275/1313 (d) 770/1313

Verify the identity sin(-x) - cos(-x) (sin x + cos x) Use the properties of sine and cosine to rewrite the left-hand side with positive arguments. sin(-x) - cos(-x) = __________ -cosx = -(sin x + cos x)

Let be an angle in standard position, with its terminal side in quadrant III such that cot θ = 4/5 Find the exact values of sinθ and cosθ. sinθ = -5√41 /41 cosθ = -4√41 /41 sinθ = -5√3/ 3 cos = -4√3/ 3 sinθ = 5√3/3 cosθ = 4√3 /3 sinθ = -5√41 /41 cosθ = 4√41 /41

Sketch the graph of the function. Include two full periods, and identify at least three vertical asymptotes. y=- (1/2)tan x

A radio transmission tower sways in a strong wind so that the top moves back and forth as much as 56 cm with a period of 6.0 s. This motion can be modeled using a sine function a) Sketch a graph of the sideways displacement of the tower, d, from its normal position as a function of time, t, for 12.0 s. b) Graph it the function (hint: you need to find amplitude period, h shift, axis of the curve if they apply to your graph)

Solve for Theta and find value of Theta 1, theta 2, theta 3, theta 4. 12.5 sin² [3π/4 cosθ] -sin² [15π/4 cosθ] = 0 On solving θ in radians θ₁ = 1.6913 (rad) θ₂ = 1.4503 (rad) θ₃ = 4.8329 (rad) θ₄ = 4.5919 (rad) Explain the steps for finding the above answers.

Solve the equation on the interval [0,2x). (tan 0-1)(sec 0-1)=0 *** Select the correct choice below and fill in any answer boxes in your choice. A. 0= (Simplify your answer. Type an exact answer, using as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no solution on this interval.