1. ## Cosine/Sine

Find the value of cos(theta) if sin(theta)=8/17 and cos(theta)<0.

I cannot seem to get the right answer but here is what I did.

Sin= Opposite/ hypoteneuse

Now I drew a right trible and labeled the angle with respect to theta. So the hypotenese was 17 and the base was 15. Now to find the right side of the triangle I applied Pathyogreans theorm (I can't spell) and set it up like this:

8^2+B^2=17^2 ; solved for b and 15.

According to me Cosine, which I am looking for should be (15/17) but somehow when I am typing the information back into the comuter system it wont accept the answer, what am I doing wrong?

Thanks

2. Hello, qbkr21!

Find the value of $\displaystyle \cos\theta$ if $\displaystyle \sin\theta = \frac{8}{17}$ and $\displaystyle \cos\theta < 0$

Here is what I did.
$\displaystyle \cos = \frac{adj}{hyp}\quad\sin = \frac{opp}{hyp}$

Now I drew a right triangle and labeled the angle with respect to $\displaystyle \theta.$
So the hypotenese was 17 and $\displaystyle opp$ was 15.
Now to find the $\displaystyle adj$ side of the triangle I applied Pythagorus' theorem

and set it up like this: .$\displaystyle 8^2 + b^2\:=\:17^2$ solved for $\displaystyle b = 15$
here!

According to me, cosine should be $\displaystyle \frac{15}{17}$, but the computer won't accept the answer.

You overlooked one of the conditions: .$\displaystyle \cos\theta < 0$
. . If $\displaystyle \cos\theta$ is negative, then $\displaystyle \theta$ is in Quadrant 2 or 3.

Since $\displaystyle \sin\theta$ is positive, $\displaystyle \theta$ is in Quadrant 1 or 2.
. . Hence, $\displaystyle \theta$ is in Quadrant 2.

Your triangle should look like this:
Code:
        *       |
| \  17 |
8|   \   |
|     \ θ
- + - - - + - -
b   |

Be very careful when using Pythagorus . . .

You had: .$\displaystyle 8^2 + b^2\:=\:17^2\quad\Rightarrow\quad b^2\:=\:225$

. . Then: .$\displaystyle b =$±$\displaystyle 15$

And you must choose the correct sign, you see.

3. ## Re:

Sir I am still confused. The system won't take the following answers I tried: -15,15, or (15/17). I am still missing a couple of pieces to this puzzle can you help me a little further?

Thanks

4. ## Re:

YES YES YES!! I got it right, that numonic device just hit me: ALL STUDENTS TAKE CALCULUS.

A: (-15/17)