SOLUTION: 1) Find the exact value of (Sin 130*)(cos 132*)+(cos 138*)(sin 132*) 2) Simplify cos [a+pi/3] 3) Find the exact value of sin (60*+45*) 4) Find the exact value of cos [pi/3

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Question 850816: 1) Find the exact value of (Sin 130*)(cos 132*)+(cos 138*)(sin 132*)
2) Simplify cos [a+pi/3]
3) Find the exact value of sin (60*+45*)
4) Find the exact value of cos [pi/3-pi/4]
5) Graph f(x) =-cos (3x+pi)
6) Graph f(x) = cos3 [x+pi/3]
7) Find the phase shift and period for the function f(x)=3sin[x/2+pi]

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
I'll just tell you how.

1) Find the exact value of (Sin 130*)(cos 132*)+(cos 138*)(sin 132*)
Use the formula sin(A+B) =sin(A)cos(B)+cos(A)sin(B)
by substituting A=132°, B=138°, then use sin(270°) = -1

2) Simplify cos [a+pi/3]
Use cos(A+B) = cos(A)cos(B)-sin(A)sin(B)
with A=a and B= then use  and 

3) Find the exact value of sin (60*+45*)
Use 
sin(A+B) =sin(A)cos(B)+cos(A)sin(B)
with A=60° and B=45° 

 and 
 and 

4) Find the exact value of cos [pi/3-pi/4]
Use cos(A-B) = cos(A)cos(B)+sin(A)sin(B)

with  and  

 and 

and

 and 

5) Graph f(x) =-cos (3x+pi)
Write as f(x) = -cos[3(x+)]

The five basic points of the graph of y=cos(x) are 

(0,1),(,0),(,-1), (,0), (,1) 

The five basic points of the graph of y=-cos(x) are found by changing
the signs of the y-coordinates of the basic five points of the
graph of y=cos(x):

(0,-1),(,0),(,1), (,0), (,-1)

The five basic points of the graph of y=-cos(3x) are found by dividing 
the x-coordinates of the basic five points of the graph of y=-cos(x)
by 3:

(0,-1),(,0),(,1), (,0), (,-1)

The five basic points of the graph of y=-cos[3(x+ from the x-coordinates 
of the basic five points of the graph of y=-cos(3x).

(,-1),(,0),(,1), (,0), (,-1)

(,-1),(,0),(,1), (,0), (,-1)

Plot those points and draw a curve through them.

6) Graph f(x) = cos[3(x+)]
That's the same problem as 5) except since it's positive,
you don't do the first step of changing the signs of the y-coordinates.

7) Find the phase shift and period for the function f(x)=3sin[x/2+pi]
Write as f(x) = 3sin(x+)

Then as f(x) = 3sin(x+)

Then as f(x) = 3sin(

Then as f(x) = 3sin[(x+)

Then use the formula:

The period of y = Asin[B(x+C)] is 
and its phase shift is 

Edwin

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