basic trigonometry problems, help?

• Feb 23rd 2009, 12:16 AM
pongpong
basic trigonometry problems, help?
given cos θ = 3/5, tan θ < 0
find:
sin 2θ
cos 2θ
cot 2θ

use half measure identities to find exact values of the following:

tan 15 degrees
sec π/12

THANK YOU SO MUCH!
• Feb 23rd 2009, 12:28 AM
Quote:

Originally Posted by pongpong
given cos θ = 3/5, tan θ < 0
find:
sin 2θ
cos 2θ
cot 2θ

use half measure identities to find exact values of the following:

tan 15 degrees
sec π/12

THANK YOU SO MUCH!

Since cos is positive and tan is negative , so the angle will be in quadrant 4 . Draw a triangle in quadrant 4 and find sin and tan .
• Feb 23rd 2009, 12:41 AM
Quote:

Originally Posted by pongpong
use half measure identities to find exact values of the following:

tan 15 degrees

tan 15 = tan 1/2(30)

You can use this identity .

$
\tan\frac{\theta}{2}=\pm\sqrt{\frac{1-cos\theta}{1+cos\theta}}
$

where $\theta$ is 30 .

In this case , $\theta$ is in the first quadrant so it will be positive .