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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

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

No clue on this one

Find the value of the trig function indicated:

22) find sin

θ if tan θ = 3/4

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

use Pythagoras to find the hypotenuse, then ...

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

Re: Finding Values of the Trig Function

Quote:

Originally Posted by

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

use Pythagoras to find the hypotenuse, then ...

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

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 $\displaystyle \displaystyle \begin{align*} \tan{\theta} \end{align*}$ for $\displaystyle \displaystyle \begin{align*} \theta \end{align*}$ in the first quadrant, he/she needs to realise that $\displaystyle \displaystyle \begin{align*} \tan{\theta} \end{align*}$ is also positive in the third quadrant, and in the third quadrant, $\displaystyle \displaystyle \begin{align*} \sin{\theta} \end{align*}$ is negative.

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

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 $\displaystyle \displaystyle \begin{align*} \tan{\theta} \end{align*}$ for $\displaystyle \displaystyle \begin{align*} \theta \end{align*}$ in the first quadrant, he/she needs to realise that $\displaystyle \displaystyle \begin{align*} \tan{\theta} \end{align*}$ is also positive in the third quadrant, and in the third quadrant, $\displaystyle \displaystyle \begin{align*} \sin{\theta} \end{align*}$ 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.