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

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