Find csc θ and sec θ, given that sin θ = − 12/13 and cos θ < 0.

Question

cscθ= ?

secθ= ?

Answer 1

cos theta<0 means cos is negative so its either the 2nd or 3rd quadrant and since sin theta-12/13 it is a negative fraction so sin is also negative sin theta<0 so then the third quadrant must be correct and the third quadrant,due to it having both negative sin and cos then tan is positive bc -/- is positive. csc is also the inverse of sin so then sin=-12/13 becomes csc(theta)=-13/12.

To find sec we need to find cos so then we need to use the Pythogorean Theorem a^2+b^2=c^2 and sin=o/h

a^2+12^2=13^2->a^2=13^2-12^2=5^2 and since cos(theta) is negative then cos(theta)=-5/13 so then sec(theta)=-13/5