Sarah Graphing

-3 cos (x-pi/4)

Amplitude -3 so it is flipped upside down and 3 tall

then phase shift pi/4 to the right


4 sin(pi/2*x-pi/2)-1

Notice this has a phase shift of -pi/2 so it moves right

Frequency is pi/2 so the period is 2 pi divided by pi/2 (6.28/1.57)

Frequency is 4.

If you look at the graph you can see that one cycle completes at 4.


Prove the identites:
2tanx/1+tan squaredx=sin2x

2tanx/sec^2 x

2 tanx * cos^2 x

2 (sinx/cosx) *cos^2 x

2 sinx * cosx

sin2x

Cotx+tanx=2csc2x

cosx/sinx + sinx/cosx

cosxcosx/sinxcosx + sinxsinx/sinxcosx

(cos^2 x +sin^2 x)/(sinxcosx)

1/sinxcosx (since 2sinxcosx= sin2x then sinxcosx = (1/2) sin(2x) )

2/sin(2x)

2csc(2x)


Solve for x
sin squaredx - cos squaredx=1/2

-cos^2 x + sin^2 x = 1/2 Use double angle formula

2cos^2 x-1= -1/2

2cos^2 x= 1/2

cos^2 x = 1/4

cos x = +or- 1/2

x = 2.09 or 1.05



2 sin squaredx - 3 cos squaredx=3