Finding Values of the Trig Function

**HelpMeTrigonometry** · April 16th 2012, 04:15 PM

Hello, Working on some Math Home work, and i am stuck.

Find the value of the trig function indicated:

6) cos θ

Finding Values of the Trig Function-triangle.png

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

**skeeter** · April 16th 2012, 04:53 PM

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 θ

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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 ...

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

**Prove It** · April 16th 2012, 06:33 PM

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

**skeeter** · April 17th 2012, 03:04 AM

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.

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