Let 0 be an angle in quadrant III such that sin 0 =-12/13. Find the exact values of sec 0 and cot 0 .

Answer 1

sinθ = -12/13

Since θ lies in quadrant 3, cosθ < 0

cosθ = -√(1 - sin²θ) = -5/13

So, secθ = 1/cosθ = -13/5 and cotθ = cosθ/sinθ = 5/12

Answer 2

-12/13=-.923

0=-67.3° 4th quad; so-90=-157.3° or 202.7°.

sec=1/cos=1/(-157.3cos)=-1.08396.....°

cot=cos/sin=2.39057.......°