# Finding Values of the Trig Function

• Apr 16th 2012, 04:15 PM
HelpMeTrigonometry
Finding Values of the Trig Function
Hello, Working on some Math Home work, and i am stuck.(Angry)

Find the value of the trig function indicated:

6) cos θAttachment 23619

would it just be 8/17?

No clue on this one
Find the value of the trig function indicated:

22) find sin θ if tan θ = 3/4
• Apr 16th 2012, 04:53 PM
skeeter
Re: Finding Values of the Trig Function
Quote:

Originally Posted by HelpMeTrigonometry
Hello, Working on some Math Home work, and i am stuck.
Find the value of the trig function indicated:

6) cos θAttachment 23619

would it just be 8/17?

yes, $\cos{\theta} = \frac{adjacent \, side}{hypotenuse}$

No clue on this one
Find the value of the trig function indicated:

22) find sin θ if tan θ = 3/4

$\tan{\theta} = \frac{opposite \, side}{adjacent \, side}$

use Pythagoras to find the hypotenuse, then ...

$\sin{\theta} = \frac{opposite \, side}{hypotenuse}$
• Apr 16th 2012, 06:33 PM
Prove It
Re: Finding Values of the Trig Function
Quote:

Originally Posted by skeeter
$\tan{\theta} = \frac{opposite \, side}{adjacent \, side}$

use Pythagoras to find the hypotenuse, then ...

$\sin{\theta} = \frac{opposite \, side}{hypotenuse}$

Even though your method is the simplest, it assumes that the answer is in the first quadrant, which it might not be. Once the OP has found \displaystyle \begin{align*} \tan{\theta} \end{align*} for \displaystyle \begin{align*} \theta \end{align*} in the first quadrant, he/she needs to realise that \displaystyle \begin{align*} \tan{\theta} \end{align*} is also positive in the third quadrant, and in the third quadrant, \displaystyle \begin{align*} \sin{\theta} \end{align*} is negative.

So there are actually two possibilities, the positive and the negative of what the OP finds using your method :)
• Apr 17th 2012, 03:04 AM
skeeter
Re: Finding Values of the Trig Function
Quote:

Originally Posted by Prove It
Even though your method is the simplest, it assumes that the answer is in the first quadrant, which it might not be. Once the OP has found \displaystyle \begin{align*} \tan{\theta} \end{align*} for \displaystyle \begin{align*} \theta \end{align*} in the first quadrant, he/she needs to realise that \displaystyle \begin{align*} \tan{\theta} \end{align*} is also positive in the third quadrant, and in the third quadrant, \displaystyle \begin{align*} \sin{\theta} \end{align*} is negative.

So there are actually two possibilities, the positive and the negative of what the OP finds using your method :)

Given the level of the question (looks like basic right triangle trig) , I kept the means of solution rather simple. Why make it more difficult for someone who asks for confirmation that their cosine ratio is correct?

I don't really believe the OP is at the level of dealing with trig functions ... yet.