Trigonometric equations Questions and Answers

Select the correct answer from each drop down menu The parent cosine function is transformed to create function d d 1 cos 211 5 To create function d the graph of the parent cosine function undergoes these transformatic horizontal shift vertical shift frequency 120 12 1242 ACEER NACENTI

A child builds two wooden train sets The path of one of the trains can be represented by the function y 2sin x 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 k 2 minutes

to answer the questions below Military time is a 24 hour clock that begins at midnight represented by 00 00 6 15pm would be written as 18 15 Date March 20 June 20 September 20 December 20 a 1 38 Day b 18 22 80 172 266 356 Sunrise 6 12am 4 42am 5 55am 7 23am Sunset in Military time 18 20 19 36 18 04 1 Using the equation y 1 38sin 13 x 80 18 22 to represent the sunset function explain in words what the following values represent 16 50 context of the sunset

2 Jada is riding on a Ferris wheel Her height in feet is modeled by the function 2am 10 h m 100 cos ride 110 where m is the number of minutes since she got on the a How many minutes does it take the Ferris wheel to make one full revolution Explain how you know b Sketch two cycles of a graph of h showing all of your thinking work 240 200 160 120 80 40

At which values in the interval 0 2TT will the functions f x 2cos20 and g x 1 4cos 0 2cos20 intersect 4 3 3 00 O C 5x W H 2n 4x 3 2 5 1

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 O 1 minute O 1 5 minutes O O W 3 minutes 3r minutes

Determine all solutions to the equation 2sin x 1 cos x on the interval 0 2TT O Ox O 5 3 6 6 2 X 5 3 3 5x 3 332 5t x 7

5TT Rewrite cos x 4 in terms of sin x and cos x

Consider the curve: y = 1-csc(2 (x-π)) (a) State the period of this curve. (b) State the phase shift of this curve, and whether it is to the right or to the left. (c) Sketch a sequence of 5 small separate graphs carefully labeled over a single period starting with y = sin(x) for x ∈[0,2π], moving one change at a time through 3 intermediate curves, and ending with the curve above, as we have done in class.

12-35. For each of the following equations, list all of the solutions without using a calculator. Use the unit circle or a graph to check your answer. Then, predict the solution that your calculator will give, and use your calculator to check your prediction. a. 2cos(x) - 1 = 0 b. 4sin²(x) - 3 = 0 c. 2sin(x) = √3

Salina, Tamara, and Uma are working on their homework together. Salina tells her friends that she has θ = 52° for the inverse cosine problem she is working on and asks if they have the same answer. Tamara says she has θ = 128°, and Uma volunteers her answer of θ = 308°. Is it possible that these are all solutions to the same problem? Justify your answer.

Suppose sin(a)= 7/10, where 0 ≤ a ≤ π/2 Find all solutions in [0, 2π): sin(2x) = 7/10

Suppose tan(a)=5/8 where 0 ≤ a ≤ π/2 Find all solutions in [0, 2π):

Solve the triangle. a = 8.387 in c= 6.216 in B=79.62°

Solve the following equation for all radian solutions and if 0 < t <2π. Give all answers as exact values in radians. Do not use a calculator. list. If there is no solution, enter NO SOLUTION.) 3 cos t = 9 cost t-3√3 (a) all radian solutions (Let k be any integer.) t=rad (b) 0≤t <2n t= rad

Given the trigonometric function defined by f(x) = cos(4x): 1. What is the amplitude of the function? _______ 2. What is the period of the function? ______ 3. Sketch one period of the function.