Finding Sin and Cot

[k1ngz16]

Let theta be an angle in quad III such that sec theta = -13/5. Find the exact values of cot theta and sin theta? Thank you guys!!

 

[stapel]

Let theta be an angle in quad III such that sec theta = -13/5. Find the exact values of cot theta and sin theta?

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

In other words, you drew the right triangle in the third quadrant, noted that both the x- and y-values will be negative, noted that the secant ratio is the reciprocal of the cosine ratio, used this information to label two of the sides of the right triangle, used the Pythagorean Theorem to find the length of the third side, and... then what?

Please be complete. Thank you!

 

[HallsofIvy]

Secant is "1 over cosine" or "hypotenuse over near side" or equivalently, on a unit circle, (x, y) such that $\displaystyle x^2+ y^2= 1$ and $\displaystyle x= -5/13$. Solve for y (in the third quadrant, y is also negative.)

"sine" is the y component and "cotangent" is x/y.