Posted by **Alex** on Tuesday, November 27, 2007 at 11:17pm.

Express as a single sine or cosine function (note: this is using double angle formulas)

g) 8sin^2x-4

I just don't get this one. I know it's got something to do with the 1-2sin^2x double angle formula. It's the opposite though? :S

h) 1-2sin^2 (π/4-x/2)

= 1-sin^2(π/4-x/2)-sin^2(π/4-x/2)

= cos^2(π/4-x/2)-sin^2(π/4-x/2)

I got all the way up to cos (π/4 - x/2 + π/4 - x/2)

The answer is supposed to be sin x. I have no clue how they got that.

- Math 2nd question -
**Reiny**, Tuesday, November 27, 2007 at 11:38pm
g) 8sin^2x-4

= 4(2sin^2 x - 1)

= 4(-cos 2x)

= -4cos 2x

h) 1-2sin^2 (π/4-x/2)

= cos 2(π/4-x/2)

= cos (π/2-x)

= cos(π/2)cosx + sin(π/2)sinx

= 0(sinx) + 1(sinx)

= sinx

- Math 2nd question -
**Reiny**, Wednesday, November 28, 2007 at 1:26am
"But can you please explain how you got 4(2sin^2 x - 1)"

I took out a common factor of 4

"..and cos 2(π/4-x/2) for h"

Ok, let's work it in reverse.

You know that cos 2A = cos^2 A - sin^2 A, or **cos 2A = 1 - 2sin^2 A** ,right?

so I simply let A = (π/4-x/2)

then 2A = 2(π/4-x/2)

= π/2 - x

## Answer This Question

## Related Questions

- Algebra2--- - 1. An artist is designing triangular mirrors. Determine the number...
- Algebra 2 .. - 1. An artist is designing triangular mirrors. Determine the ...
- Algebra 2.... - 1. An artist is designing triangular mirrors. Determine the ...
- MATH - 1.)Find the exact solution algebriacally, if possible: (PLEASE SHOW ALL ...
- Pre Calculus 12 - Another sine/cosine question i don't get in vancouver on ...
- math - Which statement is ALWAYS true? A) The sine of an angle is equal to the ...
- trig - The terminal side of an angle includes the point (5,-12). Give the sine, ...
- Math - 1) use the half-angle formulas to determine the exact values of the sine...
- Graphing trigonometric function - sine and cosine have a period 2pi tangent and ...
- Pre-Cal - 1) Use the half-angle formulas to determine the exact values of the ...

More Related Questions