SOLUTION: cos (theta-(3pi/4)) is equivalent to which of the following? a. {{{expr(-sqrt(3)/2)(cos(theta)-sin(theta))}}} b. {{{expr(-sqrt(3)/2)(cos(theta)+sin(theta))}}} c. {{{expr(-sqrt

Algebra ->  Trigonometry-basics -> SOLUTION: cos (theta-(3pi/4)) is equivalent to which of the following? a. {{{expr(-sqrt(3)/2)(cos(theta)-sin(theta))}}} b. {{{expr(-sqrt(3)/2)(cos(theta)+sin(theta))}}} c. {{{expr(-sqrt      Log On


   

Question 467094: cos (theta-(3pi/4)) is equivalent to which of the following?
a. expr%28-sqrt%283%29%2F2%29%28cos%28theta%29-sin%28theta%29%29
b. expr%28-sqrt%283%29%2F2%29%28cos%28theta%29%2Bsin%28theta%29%29
c. expr%28-sqrt%282%29%2F2%29%28cos%28theta%29%2Bsin%28theta%29%29
d. cos%28theta%29+-+sqrt%282%29%2F2
e. expr%28-sqrt%282%29%2F2%29%28cos%28theta%29-sin%28theta%29%29
f. cos%28theta%29+%2B+sqrt%282%29%2F2
Thank you sooooooooo much in advance!!! This question has been driving me bonkers;-)!!!
Found 2 solutions by lwsshak3, Edwin McCravy:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
cos (theta-(3pi/4))
..
What you have here is a cosine function of the form: y=Acos(Bx-C) with A=amplitude, period=2π/B, and phase shift=C/B
For given cosine function, y=cos(x-3π/4)
Amplitude=1
B=1
Period=2π/1=2π
Phase shift=3π/4 to the right
Ans:
What you have here is a cosine function whose value varies from +1 to -1 over one period(2π), depending on what theta(x) is.

Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor thought you wanted to graph the equation.

cos%28theta-3pi%2F4%29

Use the formula cos%28alpha-beta%29=cos%28alpha%29cos%28beta%29%2Bsin%28alpha%29sin%28beta%29

cos%28theta-3pi%2F4%29=cos%28theta%29cos%283pi%2F4%29%2Bsin%28theta%29sin%283pi%2F4%29%29

Next we use the facts that cos%283pi%2F4%29=-sqrt%282%29%2F2 and sin%283pi%2F4%29=sqrt%282%29%2F2






Factor out -sqrt%282%29%2F2

cos%28theta-3pi%2F4%29=expr%28-sqrt%282%29%2F2%29%28cos%28theta%29%2Bsin%28theta%29%29

Choice e.

Edwin