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

Algebra ->  Trigonometry-basics -> 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      Log On


   

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(20064) About Me  (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=pi%2F3 then use sin%28pi%2F3%29=sqrt%283%29%2F2 and cos%28pi%2F3%29=1%2F2

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° 

sin%28%2260%B0%22%29=sqrt%283%29%2F2 and cos%28%2260%B0%22%29=1%2F2
sin%28%2245%B0%22%29=sqrt%282%29%2F2 and cos%28%2245%B0%22%29=sqrt%282%29%2F2

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

with A=pi%2F3 and B=pi%2F4 

sin%28pi%2F3%29=sqrt%283%29%2F2 and cos%28pi%2F3%29=1%2F2

and

sin%28pi%2F4%29=sqrt%282%29%2F2 and cos%28pi%2F4%29=sqrt%282%29%2F2

5) Graph f(x) =-cos (3x+pi) 
Write as f(x) = -cos[3(x+pi%2F3)]

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

(0,1),(pi%2F2,0),(pi,-1), (3pi%2F2,0), (2pi,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),(pi%2F2,0),(pi,1), (3pi%2F2,0), (2pi,-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),(pi%2F6,0),(pi,1), (pi%2F2,0), (2pi%2F3,-1)

The five basic points of the graph of y=-cos[3(x+pi%2F3%7D%29%5D+are+found+by+subtracting+%7B%7B%7Bpi%2F3 from the x-coordinates 
of the basic five points of the graph of y=-cos(3x).

(0-pi%2F3,-1),(pi%2F6-pi%2F3,0),(pi-pi%2F3,1), (pi%2F2-pi%2F3,0), (2pi%2F3-pi%2F3,-1)

(-pi%2F3,-1),(-pi%2F6,0),(2pi%2F3,1), (pi%2F6,0), (pi%2F3,-1)

Plot those points and draw a curve through them.

6) Graph f(x) = cos[3(x+pi%2F3)] 
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%2F2x+pi%2F1)

Then as f(x) = 3sin(x%2F2x+2pi%2F2)

Then as f(x) = 3sin(%28x%2B2pi%29%2F2

Then as f(x) = 3sin[1%2F2(x+2pi)

Then use the formula:

The period of y = Asin[B(x+C)] is 2pi%22%F7%22B
and its phase shift is -C

Edwin