find the exact value when cos theta= -1/3, pi/2<theta<pi

Question

Also find sec theta, sin theta, tan theta, csc theta, and cot theta

Answer 1

The wording is confusing and the comment is correct if they want an exact value for theta. But we can proceed to the others: sketch a right triangle in quadrant II using the cosine value to label x = -1 and hypotenuse = 3. The other leg y has to be 2√2. sec θ = 1/cos θ = -3. sin θ = 2√2 /3. tan θ = -2√2. csc θ = 1/sin θ = 3 /2√2 which normalizes to 3√2 /4. cot θ = 1/tan θ = -1/ 2√2 = - √2 /4.