Cos2u=cos^2u-sin^2u cos2x=1-sin^2x Cos2u=2Cos^2U-1

Double Angle Formula

Cos2u=2Cos^2U-1 cos2x=1-sin^2x

cos2u=cos^2u-sin^2u

By: Valerie Roane

Example 1

If cos(x)=- and x is in quadrant 2, Find Cos2x and Sin2x. Use the equation: cos2u=2cos^2u-1

Plug in 2(-)^2 Then subtract 1.

Plug in - where cos is except in the front of the equation you just leave that because that's what you're trying to find.

So.. Cos2u=2(-)^2-1

=8/9-1

Cos2u=-1/9

Example 2

Find the exact value of Cos 2x if Sinx= -12/13

Use the formula: cos2x=1-sin^2x

First find the value of -12/13^2 which equals -149/169.

Simplify.

Once you get the fraction you subtract the two top numbers and cos2x will come to an exact value of -119/169.

So: cos2x=1-sin^2x =1-2(-12/13)^2 =1-2(149/169) =169-288/169

cos2x = -119/169

Example 3

Find cos60 deg. By using the functions of 30 deg.

Start with 60=2(30)

Use equation: cos2u=cos^2u-sin^2u

To take out the square of cos use the square root of 3/2.

The sin^2(30) equals ?.

Simplify all the way.

Your solution is ?.

cos2u=cos^2u-sin^2u cos60=cos(2(30))

=cos^2(30)-sin^2(30) =( 3/2)^2-(?)^2 = ?-? =2/4 =?

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