Trigonometry Questions and Answers

If cos (θ) = 8/17, 0 ≤ θ ≤ π/2, then sin(θ) equals _____ tan(θ) equals _____ sec(θ) equals _____

For 0 < θ<π/2 find the values of the trigonometric functions based on the given one.If cot (θ)=10/8then a)tan(θ)= b)sin (θ) = c)cos(θ)= d)sec (θ)= e)csc (0)=

Determine the primary trigonometric ratios for the principal angle, θ, that has a terminal arm going through the point (A, - B). Then, determine θ. (A) Draw a diagram. (B) Determine the primary trigonometric ratios - show all process work. (C) Determine e-show all process work.

Convert the radian measure to degrees. 4 4 radian(s) =

Write the following complex number in rectangular form. 6 (cos 4π/3 + i sin 4π/3)

Find the exact value of the expressions cos(a+β) sin(a+β) and tan(a+β) under the following conditions sin(a)=12/ 13, a lies in quadrant I, and sin(β)= 24/25 β lies in quadrant II. a. cos(a + β) = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression) b. sin(a+β) = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression) c. tan(a+β) = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression)

Find the area of a sector of a circle having radius r and central angle θ . r = 12.9 cm, θ = 80° The area is approximately ___ cm². (Do not round until the final answer. Then round to the nearest tenth as needed.)

Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle. 112° 30' sin(112° 30') = cos(112° 30') = tan(112° 30')=

Determine the amplitude of the function y = 2/3cos(x). Also, choose its graph. The amplitude is ___

Use the given conditions. tan(u) = -7/24, 3π/2 < u < 2л (a) Determine the quadrant in which u/2 lies. Quadrant I Quadrant II Quadrant III Quadrant IV (b) Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas. sin(u/2) = cos(u/2)= tan(u/2)=

A sinusoidal function has an amplitude of 5 units, a period of 180°, and a maximum at (0, -1). Answer the following questions. (1) Determine value of k. k = ____ (2) What is the minimum value? Min = ____ (3) What is the equation of the axis? y = ____

convert the angle measure. a)Convert 60° to radians. b) Convert 5π/4 radians to degrees.

If c is any number, then how many solutions does the equation c = tan x have in the interval (-2π,2π]? For any real number c, the equation c = tan x has___ solution(s) in the interval (-2π,2π].

Determine the amplitude of the function y = 5 sin x. Also, choose its graph. The amplitude is

determine if the side lengths form a right triangle or not. Please show all of your work and then write yes or no! 1.)21, 29, 20 2.)18, 24, 32 3.)10, 8, 6

A clock is hanging on a wall. The length of the second hand is 22 cm., and the lowest that the tip of the second hand ever reaches above the ground is h cm. The value of h is determined by the last three digits of your student number (e.g. for # 682304, h is 304 cm.) Student #:_____h: ______cm. a) What are the equation of the axis, amplitude, and period in minutes of the function that represents the tip of the second hand's height above the ground? b) Determine the equations of the sinusoidal functions (both cosine and sine) that represent the tip of the second hand's height above the ground. Assume that at t = 0, the time is 5 p.m.

Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles. sin²(2x) cos²(2x)

Title Construct a triangle given that the perimeter is 115 mm, the altitude is 40 mm and the vertical.... Description Construct a triangle given that the perimeter is 115 mm, the altitude is 40 mm and the vertical angle is 45 ° Construct a triangle with a base measuring 62 mm, an altitude of 50 mm and a vertical angle of 60°. Now draw a similar triangle with a perimeter of 250 mm.

If sin (θ) = 1/3 and is in the 1st quadrant, find cos(θ) cos(θ) = Enter your answer as a reduced radical. Enter √12 as 2sqrt(3).

If θ = 3π/4 cos(θ) = sin(θ) =

Sketch a graph of the function f(x) = 5 sin (1/2 x)

If sin (θ)=1/3 and θ is in the 1st quadrant, find cos(θ)

An object traveling at a constant angular speed requires 4.0 seconds to make one complete revolution. What is its angular speed?

If θ = 1π/6 then find exact values for the following: sin(θ) equals cos(θ) equals tan(θ) equals sec(θ) equals

Use a graphing calculator to graph Y₁, Y2, and Y₁ +Y2 on the same screen. Evaluate each of the three functions at X = 7π/6, and verify the following equality. Y₁(7π/6) + Y₂(7π/6) = (Y₁ + Y₂)(7π/6) Y₁ = cosX, Y₂ = secx Use the graphing functions of your calculator to evaluate Y₁ at (7π/6). Y₁(7π/6) = (Type an integer or decimal rounded to three decimal places as needed.) Use the graphing functions of your calculator to evaluate Y₂ at (7π/6). Y₂(7π/6) =

A rotating beacon is located at point A next to a long wall. (See the figure to the right.) The beacon is 4 m from the wall. The distance a is given by a = 4| sec 2лt|, where t is time measured in seconds since the beacon started rotating. (When t = 0, the beacon is aimed at point R.) Find a for t = 0.37. a≈ meters (Type an integer or decimal rounded to one decimal place as needed.)

The function graphed to the right is of the form y = a sec b x + c or y = a csc b x + c for some a ≠ 0, b>0. Determine the equation of the function. An equation of the function shown is y=

Given z1= -5(cos(164°) + i sin(164°)) z2= -2(cos(16°) + i sin(16°)) Find the product z1 z2. Enter an exact answer.

Given sinθ=3/4 and angle θ is in Quadrant II, what is the exact value of cosθ in simplest form? Simplify all radicals if needed.

Use a graphing calculator to graph Y₁, Y₂, and Y₁ + Y₂ on the same screen. Evaluate each of the three functions at X = (7π/6), and verify the following equality. Y₁ (7π/6) +Y₂(7π/6) = (Y₁ + Y₂)(7π/6) Y₁ = cosX, Y₂ = secX Y₁ (7π/6) = (Type an integer or decimal rounded to three decimal places as needed.) Use the graphing functions of your calculator to evaluate Y₂ at (7π/6). Y₂(7π/6)= -1.155. (Type an integer or decimal rounded to three decimal places as needed.) Use the graphing functions of your calculator to evaluate Y₁ +Y₂ at (7π/6). (Type an integer or decimal rounded to three decimal places as needed.)

Use a graphing calculator to graph Y₁, Y₂, and Y₁ +Y₂ on the same screen. Evaluate each of the three functions at X=(π/6), and verify the following equality. Y₁(π/6) + Y₂(π/6) = (Y₁+Y₂)(π/6) Y₁ = tanX, Y₂ = sec2X. Use the graphing functions of your calculator to evaluate Y₁ at (π/6). Y₁(π/6) = (Type an integer or decimal rounded to three decimal places as needed.) Use the graphing functions of your calculator to evaluate Y₂ at (π/6). Y₂(π/6) = (Type an integer or decimal rounded to three decimal places as needed.

Use a graphing calculator to graph Y₁, Y2, and Y₁ +Y₂ on the same screen. Evaluate each of the three functions at X=π/6 and verify the following equality Y₁(π/6) +Y₂(π/6)=(y₁+Y₂) (π/6) Y₁=tanX, y₂=sec2x a)Y₁(π/6)= b)Use the graphing functions of your calculator to evaluate Y₂ at (π/6) c)Use the graphing functions of your calculator to evaluate Y₁+Y₂ at(π/6)

Solve the equation in the interval [0°,360°). Use an algebraic method. 13 sin²θ - 6 sin θ = 5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is { } (Simplify your answer. Round to the nearest tenth as needed. Use a comma to separate a B. The solution is the empty set.

Convert the polar coordinate (9, π/3) to Cartesian coordinates. Enter exact values. X = y =

Convert the polar coordinate (7,π/3) to Cartesian coordinates.

Evaluating the sine of a difference of two angles can be done using sin(A - B) = ? a) sin(A) sin(B) - cos(A) cos(B) b) cos(A) cos(B) + sin(A) sin(B) c) cos(A) cos(B) – sin(A) sin(B) d) None of these

Represent the given fraction as a decimal by using the long-division algorithm. 3/8

Solve for the variable over C. Circle answers in r cis θ form. x^6 = 64i

Based on the period of f(x)=3sin(2(x-30))-4, how should the horizontal axis of the graph be scaled? Scale of 45 degrees? Scale of 60 degrees? Or scale of 22.5 degrees?

[6] Polar coordinates of a point are given. Find the rectangular coordinates of each point. Note: If is a "special" angle, then the coordinates should be exact. Otherwise, round to the nearest tenth. Sketches have been provided on the scratchwork page. (7, 150°) (-14,-7π/4) (-11,π/2) (3, 160°)

For the function f(x) = -3 sin 5(x -π/6) + 8 the vertical shift is: a) 8 units down b) 5 units up c) 8 units up d) 3 units up

The horizontal distance needed for the graph of a trigonometric function to repeat itself is called the: a) amplitude b) vertical shift c) period d) phase shift

All asymptotes to the function f(x) = csc x occur when: a) cos x = 1 b) sin x = 1 c) sin x = 0 d) cos x = 0

Which expression is equivalent to: 1 - 2 sin²(θ) a) sin²(θ)+1 b) cos² (θ) - sin²(θ) c) 1 - tan² (θ) d) 2 cos²(θ)+1

For f(x)=sinx+3 the minimum and maximum values are: a) 3 and 4 b) 1 and 2 c) 1 and 3 d) 2 and 4

The function f(x) = − tan(x) is an example of a: a) horizontal translation. b) a reflection in both the x-axis and y-axis c) reflection in the y-axis d) reflection in the x-axis

Given sin A =-6/√61 and that angle A is in Quadrant IV, find the exact value of cos A in simplest radical form using a rational denominator.

Find the exact value of sin (7π/12) a) (√3+1)/√2 b) (√3-1)/2√2 c) (1+√3)/2√2 d) (1-√3)/2√2

Find an equivalent expression to cos (x + 3π/2) a) -cos(x) b) sin(x) c) cos(x) d) -sin(x)

Which of the following expressions is equivalent to: 1/(1+ sin(θ)) + 1/(1-sin(θ)) a) 2 cos² (θ) b) 2 sec²(θ) c) cos² (θ) d) 2 csc²(θ)