## cos theta= -3/4, theta in quadrant 3. find sin theta, tan "

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
snicketycotch
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### cos theta= -3/4, theta in quadrant 3. find sin theta, tan "

jaybird0827
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### Re: cos theta= -3/4, theta in quadrant 3. find sin theta, tan "

Hmm...

$cos\,\theta\,=\,-\frac{3}{4},\,given\,\theta\,in\,Quadrant\,III$

Try this recipe:
1.) Draw a pair of coordinate axes, including labeling the axes x and y and the origin. A scale is not necessary.
2.) Draw the triangle in Quadrant III:
a.) Draw the hypotenuse of the triangle. Pick a point that is clearly in Quadrant III. Connect that point to the origin.
b.) Drop a perpendicular from the point in Quadrant III to the x-axis.
3.) Label your triangle. Since you have been given that

$cos\,\theta\,=\,-\frac{3}{4}$,

a.) Label the angle whose vertex is the origin, $\theta$
b.) Label the sides of the triangle appropriately according to the above equation; you know, SOH CAH TOA.
4.) Apply the Pythagorean Theorem to solve for the remaining side of the triangle. Label that side accordingly.
5.) Complete the following from the figure. This time use SOH CAH TOA:

$sin\,\theta\,=$

$tan\,\theta\,=$

You should be able to do the exercise now. If you get stuck, please reply showing which of the above steps you were able to complete.