Objective Sectio Sample Problem n Express angles in 10.1 1. degrees and a) Convert 240 to radians radians on the b) Find a positive coterminal angle and a negative coterminal angle unit circle c) Graph the angle in the coordinate plane Evaluate the six 10.2 2. a) What is the reference angle for e = circular functions: sine, cosine, b) Find the exact value of the six circular functions of 0 = (no tangent, secant, decimals are allowed) cosecant and cotangent for standard angles using the unit circle Evaluate the six 10.3 3. If cos 0 = ; and 0 is in Quadrant IV, find the other five trig circular functions: functions. Give exact answers (no decimals allowed). sine, cosine, tangent, secant, cosecant and cotangent for any angle Use ratio, 10.4 4. Use ratio, reciprocal and/or Pythagorean Identities to prove: reciprocal and a) cos 0 csco = cote Pythagorean bj - sin e = cote Identities sec 8-cos e Use sum and 10.4 5. If sin 0 = = with 0 in Quadrant II, find the following difference, a) sin (20) double-angle, half-angle and b) cos () product to sum formulas for trig functions.Use sum and difference, doubleangle, and halfangle formulas for trig functions. a . . . 12 . . 6. For coso: E Wlth a In Quadrantl and Sin}? 13 with ,8 In Quadrant "I. Find the following exact values {no decimals allowed}. a} sin (or ,8] b} tan[ or + {3) Use sum and difference, doubleangle, and half-angle formulas for trig functions. 7'. Prove the following identitv 1 cos[2a) sin (2n) = tan (a) Graph trigonometric functions using properties such as amplitude, period, vertical shift and phase shift Graph trigonometric functions using properties such as amplitude, period, vertical shift and phase shift "I 8. For the function: 3! = 8 sin (2.x 3) 3 a} Find amplitude b} Find the period c} Find the vertical shift d} Find the phase shift e}l Graph one period of the functions using appropriate markings on the x and vaxis 9. a} Give the equation for the trigonometric function shown in the graph 3 \ z\3mm\ b} What is the period of the function c} 1|l'lr'hat is the phase shift? Use inverse 10.6 10. Find the following angles trigonometric functions to find a) sin 1 (-;) angles. b) cos-1 ( _ Vz c) sin(cos -1 Solve right- 10.6 11. triangle When I stand 30 feet away from a tree at home, the angle d application problems is 50 and the angle of depression to the base of the tree is tree? Round your answer to the nearest foot. Solve 10.7 12. Find all solutions to the following equations on [0,2x) trigonometric a) 18 sin e cos 8 = 6 sin 0 equations b) 4 cos(2x) = 4 sin(x) + 3Solve trigonometric inequalities Solve applications of periodic functions 13. Solve the following inequalities on [Cl,2rt) a] 2 sing s: 1.5 h} 2 cos 9 E 1 14. Outside temperature over a dag.r can be modelled as a sinusoidal function. Suppose you know the high temperature for the day.r is 34 degrees and the lot-'r temperature of 4a degrees occurs at 3 Mil. assume that t is the number of hours since midnight. lit} Graph this function over a 24 hours period E] Find an equation for the temperature, I), in terms of t. Solve general triangles using the Law of Sines Solve general triangles using the Law of Cosines Find area of general triangles Solve application problems using the Law of Sines and Lair.r of rCosines 15_ Solve the triangle ABC if b = 125i, c = 169, AB = 40. 16. In the triangle shown, - length A0 = 10 - length RC = 9 . angle C = 52 degrees Find the measures of side AB. 1?. Given the triangle 2'5 23 . find the area of the triangle. 13. it pilot is flying over a straliht "WEE He determines the angles at depression to twp mileposts. 4.9 ml apart. to be 311' and 41'. as shown in the figure. _____ iiiET'UEMm , 4.9m." -. fl 3 How high above the ground is the airplane. Convert between 11.4 19. polar coordinates Rewrite the polar equation r = 6 sin(0) as a Cartesian equation. and rectangular coordinates Graph functions 11.5 20. Draw the following polar graphs in polar a) r = 4 - 4 sin 0 coordinates b) r = 5 sin(20) Find points of 11.5 21. Find the points of intersection of the following polar curves intersection of r = 6 cos(20) and r = 3 polar graphsConvert complex numbers to polar form 22. Convert the following complex number in polar {cis} form z=l~.ft' Multiply, divide 23. For the two complex numbers: 21 = 2 + 21' and 22 = 4i and use Convert each to polar form. Find the following: exponents on a] 2122 complex h} '11 numbers in polar 2'5, Cl 31 form Find roots of 24. For the complex numbers: 2 = r1 4t complex Find the v3 numbers in polar form Perform 25. operations on vectors such as: addition and scalar multi lication. Find magnitude and angle orientation of VECtDI'S Find dot product and angle between vectors Write equations in parametric form and graph equations in parametric form Let a = {4, 2> and 3 = (3, 3). Find 35 3. 26. a] For the following vector, convert from magnitude and direction to x and v coordinates r = 5.9 = 330" b} For the following vector, convert from x and v coordinates to ma-nitude and direction