Objective Sectio Sample Problem n Express angles in 10.1 1. a) Convert 240 to radians b) Find a positive coterminal angle and a negative coterminal angle c) Graph the angle in the coordinate plane degrees and radians on the unit circle Evaluate the six 10.2 S 2. a) What is the reference angle for = circular functions: sine, cosine, tangent, secant, cosecant and cotangent for 3 b) Find the exact value of the six circular functions of = decimals are allowed) ST (no standard angles using the unit circle Evaluate the six 10.3 circular functions: sine, cosine, tangent, secant, cosecant and cotangent for any 3. If cos e = and is in Quadrant IV, find the other five trig functions. Give exact answers (no decimals allowed). angle Use ratio, reciprocal and 10.4 Pythagorean Identities Use sum and 10.4 difference, double-angle, half-angle and product to sum formulas for trig functions. 4. Use ratio, reciprocal and/or Pythagorean Identities to prove: a) cos csc b) sin sece-cos = cot = cot e 5. If sin within Quadrant II, find the following a) sin (20) b) cos (-) 12 Use sum and difference, double-angle, and half-angle formulas for trig 10.4 6. For cos = with a in Quadrant I and sin = - 13 with in B Quadrant III. Find the following exact values (no decimals allowed). a) sin ( - ) b) tan( a + ) functions. Use sum and 10.4 7. Prove the following identity difference, 1 - cos(2a) sin (2a) =tan (a) double-angle, and half-angle formulas for trig functions. Graph trigonometric functions using properties such as amplitude, period, vertical shift and phase shift Graph trigonometric functions using 10.5 - 8. For the function: y = 8 sin (2x ) 3 a) Find amplitude b) Find the period c) Find the vertical shift d) Find the phase shift e) Graph one period of the functions using appropriate markings on the x and y-axis 9. a) Give the equation for the trigonometric function shown in the graph properties such as amplitude, period, vertical shift and phase shift -3/2 - -2 J/2 3/2 -1 b) What is the period of the function c) What is the phase shift? Use inverse trigonometric functions to find 10.6 10. Find the following angles a) sin (-) b) cos (-) c) sin (cos-1 ()) 2 When I stand 30 feet away from a tree at home, the angle is 50 and the angle of depression to the base of the tree is tree? Round your answer to the nearest foot. 12. Find all solutions to the following equations on [0,2) a) 18 sin cos 0 = 6 sin 0 b) 4 cos(2x) 4 sin (x) + 3 = angles. Solve right- 10.6 11. triangle application problems Solve trigonometric 10.7 equations 13. Solve the following inequalities on [0,2) a) 2 sin 0 Rewrite the polar equation r = 6 sin (0) as a Cartesian equation. Convert between 11.4 polar coordinates and rectangular coordinates 19. Graph functions 11.5 in polar coordinates Find points of 11.5 intersection of polar graphs 20. Draw the following polar graphs a) r4 4 sin b) r = 5 sin(20) 21. Find the points of intersection of the following polar curves r = 6 cos(20) and r = 3