# Compound Angle Formulas Determining Exact Value of Trigonometric Ratio Help!?!?!?!

• Nov 28th 2009, 02:47 PM
TheCB4
Compound Angle Formulas Determining Exact Value of Trigonometric Ratio Help!?!?!?!
I am having alot of trouble with this particular question

Determine the exact value of each trigonometric ratio.

1) Tan 23pi/12

answer in my book says 2 + square root 3

Thank you
• Nov 28th 2009, 02:51 PM
mr fantastic
Quote:

Originally Posted by TheCB4
I am having alot of trouble with this particular question

Determine the exact value of each trigonometric ratio.

1) Tan 23pi/12

answer in my book says 2 + square root 3

Thank you

For starters, the answer is meant to be negative since 23pi/12 lies in the 4th quadrant.

Note that:

1. $\displaystyle \tan \frac{23 \pi}{12} = - \tan \frac{\pi}{12}$ by symmetry of the unit circle.

2. $\displaystyle \frac{\pi}{12} = \frac{\pi}{3} - \frac{\pi}{4}$ so using the compound angle formula is suggested ....
• Nov 28th 2009, 03:47 PM
TheCB4
Hi but the main trouble i am having is using the compound angle formula of tan, do you think you can show me how to use it, it would be great?

Quote:

Originally Posted by mr fantastic
For starters, the answer is meant to be negative since 23pi/12 lies in the 4th quadrant.

Note that:

1. $\displaystyle \tan \frac{23 \pi}{12} = - \tan \frac{\pi}{12}$ by symmetry of the unit circle.

2. $\displaystyle \frac{\pi}{12} = \frac{\pi}{3} - \frac{\pi}{4}$ so using the compound angle formula is suggested ....

• Nov 28th 2009, 06:06 PM
mr fantastic
Quote:

Originally Posted by TheCB4
Hi but the main trouble i am having is using the compound angle formula of tan, do you think you can show me how to use it, it would be great?

Please show all your work and say exactly where it is that you get stuck.