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Name:_______________________________________________________ Date:__________ Period:_______ Trig Equations Test 1: Review Sheet Algebra 2 HONORS Trig Equations Test 1: Review Sheet Complete all work on a separate sheet of paper. Angle Sum & Difference: Find the exact value of the following: 1.) 2.) 3.) 4.) 5.) 6.) 7.) If is the value of and and a is in Quadrant III and b is in Quadrant I, what ? 8.) Evaluate the expression given that and , with y in Quadrant III. 9.) If value of and . and both a and b are positive acute angles, find the 10.) If A and B are positive acute angles, of ? 11.) If 12.) If and , with x in Quadrant II, , and , what is the value of , where x is in Quadrant I, find the value of 13.) The expression is equivalent to (1) sinx (2) –sinx (3) cosx 14.) The expression (1) (2) 15.) The expression (1) cosA (2) –cosA (4) –cosx is equivalent to (3) (4) is equivalent to (3) sinA (4) –sinA , what is the value ? . Double Angle: 16.) If , what is the value of 17.) If is a positive acute angle such that ? , what is the value of ? 18.) If , what is ? 19.) If , and <A lies in Quadrant IV, find the value of 20.) and <A is in Quadrant I. Find, in simplest form, the value of . . 21.) The expression (1) sin60 (2) cos60 has the same value as (3) cos15 (4) sin15 22.) The expression (1) sin20 (2) sin80 has the same value as (3) cos80 (4) cos20 23.) The expression (1) (2) has the same value as (3) (4) Half Angle: 24.) If x is a positive acute angle and 25.) If 26.) If 27.) If , what is the value of , what is the positive value of ? , and x is an angle in Quadrant I, find , find the positive value of ? . . Linear Trig Equations: Solve for all values of , to the nearest degree, in the interval 0° ≤ < 360°. 28.) 6(tan + 2) = 6 29.) 6sin – 3 3 = 0 30.) 5sec + 4 = 3sec 31.) 3 cos θ = cos θ – 1 32.) -2 sin θ – 2 =0 34.) 3(sin θ – 1) = 0 35.) cot θ + 2 = 2 cot θ + 3 33.) 3 cos θ + 5 = 0 and Quadratic Trig Equations: Solve for all values of , to the nearest degree, in the interval 0 ≤ 36.) cos2 + 7cos – 8 = 0 37.) tan2 + tan = 12 38.) 2sin2 + 20 = 22sin 39.) sin cos + cos = 0 40.) 2sin2 + 4sin = 0 41.) cot2 = 7cot – 10 42.) csc2 – 18 = 3csc 43.) cos2θ – cos θ = 0 44.) sin2θ + 3 sin θ + 2 = 0 45.) cos2θ – 2 cos θ = 3 <2 . 46.) sec2θ = sec θ + 2 Case II: Solve for all values of , to the nearest degree, in the interval 0° ≤ 47.) 2tan2 - 3tan – 5 = 0 48.) 12cos2 – 3 = 5cos 49.) 5sin2 + 26sin + 5 = 0 50.) 8tan2 = 22tan – 15 51.) 3sec2 – 11sec = 4 52.) 10csc2 + 21csc + 8 = 0 Quadratic Formula: Solve for all values of , to the nearest degree, in the interval 0° ≤ 53.) 4sin2 + 3sin – 7 = 0 54.) tan2 + 11 = 7tan 55.) 2cos2 = 5cos + 1 56.) 3sec2 + 9sec = 5 < 360°. < 360°. Review Questions: 57.) Determine the solution set for the following system of equations: 58.) Determine the nature of the roots of the equation . 59.) The discriminant of a quadratic equation is 24. Describe the nature of the roots. 60.) For which positive value of m will the equation that are real, equal, and rational? (1) 12 (2) 9 (3) 3 (4) 4 have roots 61.) Find all value of k such that the equation has imaginary roots. 62.) Factor the expression completely . 63.) Factor completely: 64.) Find the solution set to the equation . 65.) What is the solution set to the equation ? 66.) What is the solution set for the equation ? 67.) Rationalize: 68.) What is the product of and its conjugate? 69.) Find the product of and its conjugate. 70.) Sketch an angle of 240o in standard position. Then find the exact value of sin240o. 71.) What is the solution set to the equation 72.) Find the roots of the equation ? . 73.) The probability that Peter will get a 100 on his math test is 72%. To the nearest thousandth, what is the probability that Peter will get a 100 on at least 3 out of the next 5 math tests? 74.) The probability that it will snow on any given day is 12%. To the nearest tenth of a percent, what is the probability that it will snow at most 2 out of 6 days? 75.) How many different 8 different letter arrangements can be made by using the letters in “STANDARD”? Answer Key: 1.) 2.) 3.) 4.) 5.) 6.) 7.) 8.) 9.) 10.) 11.) 12.) 13.) (2) 14.) (4) 15.) (4) 16.) 17.) 18.) 19.) 20.) 21.) (2) 22.) (3) 23.) (3) 24.) 25.) 26.) 28.) {135°,315°} 29.) {60°,120°} 30.) {120°,240°} 31.) {120°,240°} 32.) {225°,315°} 33.) No solution 34.) {90°} 35.) {135°,315°} 36.) {0} 37.) 38.) 39.) 40.) 41.) 42.) 43.) 44.) 45.) 46.) 47.) {68°,135°,248°,315°} 48.) {41°,109°,251°,319°} 49.) {192°,348°} 50.) {51°,56°,231°,236°} 51.) {76°,284°} 52.) {219°,321°} 53.) {90°} 54.) {67°,78°,247°,258°} ; 27.) 55.) {101°,259°} 56.) {107°,253°} 57.) (0,-6) & (4,6) 58.) imaginary 59.) real, irrational, unequal 60.) (1) 61.) 62.) 63.) 64.) 65.) 66.) 67.) 68.) 117 69.) 70.) 71.) 72.) 73.) 0.862 74.) 97.4% 75.) 10080