Trigonometric Functions

Suppose that 0 is an acute angle of a right triangle and that sec(0) = Find csc(0) and tan(0). a) O csc(0) = V33 V33 7 ' tan(0) = 4 b) O csc(0) = 1V33 tan (0) = 433 33 33 433 c) O csc(8) = 733 33 tan(0) 33 d) O csc(0) = 33 33 tan(0) = 4 7 e) O csc (0) = 733 33 tan(0) = V33 4 f) O None of the above.3 3 Simplify the following expression: + sec(ac) - 1 sec(x) + 1 a) 0 6 sec(x) cot(x) b) O 6 sec(x) cot2 (a) c) O 6 csc(x) tan(x) d) O 6 cos(a) sin? (ac ) e) O 6 cot2 (x) f) O None of the abovetan? (a) + cot"(a) = 7, find the value of: (tan(a) + cot(a)) a) O 10 b) 07 c) 09 d) O 11 e) 0 8 f) O None of the aboveRight triangles ABC and BOD with right angle 0 are given below. It mZA = 30, mil) 2 45\l KLM is a triangle with muff) : 303. If KL : 20 units, and tan(M) : 5 then find the length of KM. Hint: Draw a picture and include the altitude from the angle L to the side KM. a) 10+20 b) 10\\/3+1U 21 '6 c) 2 d) 10 J3 + 5 e) 30 f} None of the above ABC is a right triangle with right angle 0. If m(A) : 6t]3 and the hypotenuse is 9 units long, find the area of this triangle. 81 a) 8 81 \\/3 b) 2 81 c) 3 81 E d) 4 81 e) I f} None of the above In right triangle ABC with right angle C, AB = 13, and AC= 6, find sin(A) and cot(A). a) O sin(A) _ V133 , cot( A) _ V133 13 6 b) O sin(A) = V133 6 cot(A) = 6133 133 6 c) O sin (A) = , cot( A) = 6133 13 133 d) O sin (A) = 13 , Cot ( A) = V133 6 e) O sin(A) = V133 13 cot (A) = 6133 133 f) O None of the above.In the figure below, angle B is a right angle, mZBAC = 30 and the length of AC= 12. If CD = 5, find the length of AD. Note: The triangle may not be drawn to scale. A 309 B C D a) O 229 b) 0 2 229 c) O 458 d) 06 e) O V229 f) O None of the above.A car has wheels with a 4 inch radius. If each wheel's rate of turn is 3 revolutions per second, nd the angular speed in units of radians/second. a) 12 71' b) 6 11' c) 3 7r E d) 4 3 7r 9' Y f} None of the above. Let P (x, y) denote the point where the terminal side of an angle - meets the unit circle. If P is in Quadrant IV and @ = find tan(0). a) b) O 9 C) 16 d) O e) f) O None of the above.Which of the following is equivalent to: (2 sin(x) + 2 cos(a) )? ? a) O 2 + 2 sin(x) b) O 4 + 2 sin(x) cos(x) c) 0 4 + 4 sin(x) cos(x) d) O 2 + 2 sin(x) cos(x) e) O 4 + 8 sin(x) cos(x) f) O None of the above