Posted by **trista** on Tuesday, February 24, 2009 at 6:48pm.

use the half angle formula to determine the exact values of sin, cos, and tan of the angle.

pie/8

and

pie/12

- precal -
**bobpursley**, Tuesday, February 24, 2009 at 6:55pm
I will be happy to check your thinking on this.

- precal -
**trista**, Tuesday, February 24, 2009 at 7:02pm
i honestly don't know what to do or how to start anyways

- precal -
**Reiny**, Tuesday, February 24, 2009 at 8:37pm
the half-angle formulas let you split an angle in half

there is sin 2A = 2sinAcosA and

cos 2A = cos^2 A - sin^2 A or

cos 2A = 2cos^2 A - 1 or

cos 2A = 1 - 2sin^2 A

I will do the pi/12 angle for you.

pi/6 rads = 30 degrees, and pi/12 = 15 degrees

From the 30-60-90 triangle you should know

sin30 = 1/2 and cos30 = ?3/2

cos 30 = 1 - 2sin^2 15

2sin^2 15 = 1-?3/2

sin ^2 15 = 1/2 - ?3/4

= (2-?3)4

so sin 15 = ?(2-?3)/2

or sin pi/12 = ?(2-?3)/2

now ;use the other version of cos 2A to get cos pi/12

and since tanx = sinx/cosx, divide the two results to get the tangent.

verify your answer with your calculator

for the first pi/8 is half of pi/4 which is 45 degrees

you should know the trig rations for 45 degrees.

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