Trigonometric equations Questions and Answers

Solve the following equation for x, where 0 < x < 2π. 6 cos (2x) + 18 cos x - 24 = 0 Select the correct answer below:

Solve the following equation on the interval [0, 360°). 2 cos (3x) -√3 = 0 The answer choices below represent solution sets. Choose the answer that represents the entire solution set on the given interval. Select the correct answer below: {30°, 110°, 330°} {30°, 120°, 210°, 330°} {20°, 140°, 260°, 340°} {20°, 100°, 140°, 220°, 260°, 340°} {10°, 130°, 250°, 330°} {10°, 110°, 130°, 230°, 250°, 350°} There are no solutions to this equation

If 4sin²θ-9 = -7, where 0 ≤ θ < 2π, what are the values of ? List your answers as exact answers in terms of π, separated by a comma if necessary. Provide your answer below:

cotx/CSCX = 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.

Use a power reducing formula to determine which of the following is equivalent to 32sin4θ. Select the correct answer below: 8 + 16cos (4θ) 12 16cos (2θ) + 4cos (4θ) 12+16cos (2θ) + 4cos (4θ) 24 16cos (2θ) + 16cos (4θ)

(1 point) Determine all solutions for cos(0) = 0.39 Solutions with base angle in quadrant I: 0 Solutions with base angle in quadrant IV: 0 = where n is any integer, and both base angles are between 0 and 2. Use radian measure and enter your answers using at least four significant digits.

Which of the answer choices given below is an equivalent expression for sin² (3x) that doesn't contain any powers of sine or cosine greater than 1? Select the correct answer below: O 1 - cos(6x) O1/2cos (3x) O 1/2+ cos(3x) O1/2 + cos(6x) O1/2-cos(6x)

the equation for exact solutions over the interval [0, 2x). 3 tan 3x=3 Solve ww*** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution set is (Type an exact answer, using z as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a comma t separate answers as needed.) OB. The solution is the empty set.

3. Solve each of the following on the interval € [0,2π]. a. cosx + 0.45 = 0 (4 marks) sulay imunizem 5 bas - 10 eulsy murzinin saat ou lesinev s frignal OU (mhamn 2) noon ods b. 2sec²x - 8 = 0 (6 marks) antwolle) orbylinishi 3-** c. 2sin²x - sinx-1=0 (6 marks)

Find the exact values of s in the interval [0,2x) that satisfy the condition, sin s= -1/2 (Use a comma to separate answers as needed. Simplify your answers. Type exact answers, using as needed. Use integers or fractions for any numbers in the expression.)

Correct Solve the following equation on the interval [0°, 360°). Round answers to the nearest tenth. If there is no solution, indicate "No Solution." 12cos(x) = 3sec(x) - 5 Answer How to enter your answer (opens in new window) Enter your answer in degrees in the box below. Multiple solutions should be separated by commas. Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used. x= No Solution

Determine the point(s) at which the given function f(x) is continuous. f(x) = 6 csc (6x) The function is continuous on (-∞,∞) except for (Type an exact answer, using as needed. Type an expression using n, where n is an integer.)

Consider the equation sin((x + y)) = 0. a) Use your understanding of the sine function to find the solutions to the equation. b) Plot the solutions to the equation. c) Use implicit differentiation to check the slopes of the lines from part b.

Roger is standing next to a tree where his shadow is 3 feet long and the shadow of the tree is 18 feet long. If Roger is 4. 5 feet tall, what is the height of the tree? A. 12 ft B. 16.5 ft C. 19.5 ft D. 27 ft

The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after 0 seconds can be described by the function f(θ) = 2cos θ+√3. Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function? Part C: A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g(θ)=1-sin²θ+√3. At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal?

Solve the following equation on the interval [0,2π). cos x − 2 sin x cosx=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x = (Type an exact answer, using as needed. Use a comma to separate answers as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression.) B. There is no solution.

A seismograph measures the movement of the earth during an earthquake. During a tremor, the motion of the earth can be measured by: s(t) = 7 cos(2/t) where t is the time in seconds. Determine the rate of change of the ground's position at 4 seconds.

Which equation represents a tangent function with a domain of all Real numbers such that x≠π/4+π/2n, where n is an integer? f(x)=tan(2x - π) g(x)=tan(x - π) h(x)=tan(x-π/2) j(x)=tan(x/2-π)

Use a calculator to perform the indicated operations. Write the answer in rectangular form (12 cis 80.5°)(5 cis 74.5°)

What is the amplitude and period of the function f(x) = 2 sin(1/5 x)? Please provide your answer in the form of π. Provide your answer below:

On the graph of f(x) = cos x and the interval [2, 4π), for what value of x does f(x) achieve a minimum? Choose all answers that apply. Select all that apply: 0 - ▬ ■ 2π 57 3π E2 7/2

Find the exact value of y, or state that y is undefined. y = cos^-1(10) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. cos ^-1(10) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. B. The answer is undefined

You are given that sin(A) = -3/5, with A in Quadrant III, and cos(B) = 24/25, with B in Quadrant I. Find sin(A + B). Give your answer as a fraction. Provide your answer below: sin (A + B)=

Given that cos θ = -24/25 and sin θ<0, determine the values of the sine and cosine functions for 2θ sin 2θ= cos 2θ= (Type an intege for a simplified fraction.)

Use a power reducing formula to simplify 20cos^4 x. Write your answer as an equivalent expression that does not contain any powers of sine or cosine greater than 1.

Solve the equation for exact solutions over the interval [0, 2x). 4sin2x+8sin x+4=0 Select the correct choice below and, if necessary, fill, in the answer box to complete your choice. A. The solution set is { } (Type an exact answer, using x 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. The solution is the empty set.

The position of an engine's piston, in inches, is given by the trigonometric function p(t) = 2 sin (200πt), where t represents the time in seconds. The of the function equals 2. amplitude midline frequency period

Identify the function's midline, amplitude, and period. f(x) = 2 sin(x) +1 Midline: y = 1 Amplitude: 2 Period: 2 Midline: y = 1 Amplitude: None Period: 2 Midline: y = 1 Amplitude: 2 Period: 1 Midline: y = 0 Amplitude: 2 Period: 27

Solve the equation for solutions in the interval [0,2). Use algebraic methods and give exact values. Support your solutions graphically. sin (x/2) = √3 - sin(x/2)

The distance from the ground, in meters, of a person riding on a Ferris wheel after t seconds can be modeled by the function D(t)=20 sin(t/10)+20. Based on the graph of the function that represents the rider's distance from the ground, how long will it take before the rider is at the lowest point on the Ferris wheel? 5nseconds 10n seconds 15n seconds 20n seconds

A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 24 seconds, and the average height of the bottle is 8 feet. The bottle moves in a manner such that the distance from the highest and lowest point is 4 feet. A cosine function relation to the height. model the movement of the message in a bottle in Part A: Determine the amplitude and period of the function that could model the height of the message in a bottle as a function of time, t. (5 points) Part B: Assuming that at t=0 the message in a bottle is at its average height and moves upwards after, what is the equation of the function that could represent the situation? Part C: Based on the graph of the function, after how many seconds will it reach its lowest height?

A child builds two wooden train sets. The path of one of the trains can be represented by the function y=2sin2x, where y represents the distance of the train from the child as a function of x minutes. The distance from the child to the second train can be represented by the function y = 3-sin x. What is the number of minutes it will take until the two trains are first equidistant from the child? 1 minute 1.5 minutes π/2 minutes π/3 minutes