# Math 2nd question

posted by .

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 -

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 -

Thanks a lot!
But can you please explain how you got 4(2sin^2 x - 1) for g and cos 2(π/4-x/2) for h?

I think I might understand h because 1-sin^2x = cosx but wouldn't it just be cos(π/4-x/2) cos(π/4-x/2)?

• Math 2nd question -

"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

## Similar Questions

1. ### MATH

1.)Find the exact solution algebriacally, if possible: (PLEASE SHOW ALL STEPS) sin 2x - sin x = 0 2.) GIVEN: sin u = 3/5, 0 < u < ï/2 Find the exact values of: sin 2u, cos 2u and tan 2u using the double-angle formulas. 3.)Use …
2. ### trig

The terminal side of an angle includes the point (5,-12). Give the sine, cosine, and tangent of the angle exactly. I know how to plot it and everything, but I'm not sure where to put theta so I know which angle to use for finding sine, …

Use the Pythagorean identity to show that the double angle formula for cosine can be written as a) cos2x = 1 - 2sin^2x b) cos2x = 2cos^2x - 1
4. ### trig

A coil of wire rotating in a magnetic field induces a coltage E=20sin((PIa/4) - (PI/2)). Use an identity to express this in terms of cos(PIa/4). Types of Identities: Double Angle, Half Angle, Sum and Difference of Sine, Cosine, and …
5. ### precalculus

write each expression as the sine, cosine or tangent of a double angle. then find the exact value of the expression. a. 2sin 22.5 cos 22.5 b. cos^2 105- sin^2 105
6. ### Algebra 2....

1. An artist is designing triangular mirrors. Determine the number of different triangles that she can form using the given measurements. Then solve the triangles. Round to the nearest tenth. a=4.2 cm b= 5.7 cm measure angle A= 39 …
7. ### Algebra 2 ..

1. An artist is designing triangular mirrors. Determine the number of different triangles that she can form using the given measurements. Then solve the triangles. Round to the nearest tenth. a=4.2 cm b= 5.7 cm measure angle A= 39 …
8. ### Algebra2---

1. An artist is designing triangular mirrors. Determine the number of different triangles that she can form using the given measurements. Then solve the triangles. Round to the nearest tenth. a=4.2 cm b= 5.7 cm measure angle A= 39 …
9. ### math

Which statement is ALWAYS true? A) The sine of an angle is equal to the sine of the angle's complement. B) The cosine of an angle is equal to the sine of the angle's supplement. C) The sine of an angle is equal to the cosine of the
10. ### pre calculus

Double Angle Formula. If the double angle formula for cos2(u) = 2cos^2(u)-1, then write the double angle formula for cos2(u) in terms of sine.

More Similar Questions