Question

If tan theta = 4/3 , and lies in the third quadrant , write the correct ratio for sin theta , cos theta , sec theta , csc theta , and cot theta

Answer 1

Tan∅=4/3

SohCahToa...
Sine=Opposite/Hypotenuse
Cosine=Adjacent/Hypotenuse
Tangent=Opposite/Adjacent

Opposite=4
Adjacent=3

BUT, since it's in the third quadrant, they're both negative.

Opposite=-4
Adjacent=-3

Solve for the hypotenuse.... (-4)²+(-3)²=c²

c=5

Sine=-4/5
Cosine=-3/5
Secant=-5/3
Cosecant=-5/4
Cotangent=3/4