Thread: 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.

Cos= adjacent/ hypoteneuse
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

Hello, qbkr21!

Find the value of if and

Here is what I did.


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

and set it up like this: . solved for ← here!

According to me, cosine should be , but the computer won't accept the answer.

You overlooked one of the conditions: .
. . If is negative, then is in Quadrant 2 or 3.

Since is positive, is in Quadrant 1 or 2.
. . Hence, is in Quadrant 2.

Your triangle should look like this:

Code:

        *       |
        | \  17 |
       8|   \   |
        |     \ θ
      - + - - - + - -
            b   |

Be very careful when using Pythagorus . . .

You had: .

. . Then: . ±

And you must choose the correct sign, you see.

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

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

A: (-15/17)