39. P(2, 3) is on the circle with center O(0, 0). a. Write an equation of the circle. b. Write an equation for the tangent / to the circle at P. (Hint: 1 is perpendicular to OP.) 7. Find an equation for the hyperbola that satisfies the given conditions. 6-4 a. Center at (0, 0), a vertex at (0, -3), and a focus at (0, -V13) VLU Simplify. Simplify each expression. 13. sin x cos x 1. a. cos 0 + sin2 0 1 - cos x 25. Use the equation sin' 0 + cos' 0 = 1 to prove that tan' 0 + 1 = sec' 0. 26. Use the equation sin 0 + cos? 0 = 1 to prove that cot 0 + 1 = csc? 0. 5. A sector of a circle has area 25 cm and central angle 0.5 radians, Find its radius and are length, 4. State whether each expression is positive or negative. a. sin 1659 b. sin 2650 C. COS 210 d. cos 3109 17. cot- 0 - + sin 0 csc 0 1 + csc 0 29. cot 0 + cos2 0 + sin? 0 = csc- 0 31, sin & cos = sin @ csc 0 csc 0 sec 0