If sin theta = 2/7 and theta is in quadrant 2 find cos theta, sec theta, csc theta, tan theta, and cot theta.

Question

If sin theta = 2/7 and theta is in quadrant 2 find cos theta, sec theta, csc theta, tan theta, and cot theta.

Answer 1

sinθ = 2/7;  then 1 = sin^2 θ + cos^2 θ => cos^2 θ = 1- 4/49 = 45/49 = (3√5)/7. is negative because the angle is in the second quadrant.

Tan θ = sinθ/cosθ = (2√5)/15 negative

cot θ = cosθ/sinθ = (3√5)/2 negative

sec θ = 1/cosθ =    ................negative

cosecθ = 1/sinθ = ................ positive.