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Name: ________________________ Pre-Calculus Honors Fall Final Exam Review *** ALL WORK AND ANSWERS MUST BE ON NOTEBOOK PAPER *** 7 to degrees. 2) Convert 115o to radian measure. 8 3) Determine two co-terminal measures 4) Determine two co-terminal measures 3 for for -36o. 8 5) A sprinkler n a golf course fairway is set to spray water over a distance of 70 feet and rotates through an angle of 120o. Find the area of the fairway watered by the sprinkler. 1) Convert 6) A terminal ray passes through (12, -5). Find the value to all six trig. functions. 8) Evaluate each: cos 3 5 3 , sin , tan 4 6 2 7) Find the value to all six trigonometric 5 functions if = . 3 11 5 9) Evaluate each: csc , sec , cot 6 4 1 10) If sin and , find 11) Evaluate cot 52.8o. 3 2 the remaining 5 trig functions. 12 – 15: Solve for x in each right triangle. 12) 13) 14) x 12o 36 63o x x 7.5 2 15) 31 20 34 x 16) A steel cable zip-line is being constructed for a competition on a reality television show. One end of the zip-line is attached to a platform on top of a 150 foot pole. The other end of the zip-line is attached to the top of a 5 foot stake. The angle of elevation to the platform is 23o. How long is the zip-line? 11 17) Find the reference angle if = 309o. 18) Find the reference angle if . 3 19) Determine the quadrant when sec < 0 20) Find all solutions in 0 < < 2 for 3 sin and csc < 0 . 2 21) Find all solutions in 0 < < 2 for 22) Find all solutions in 0 < < 2 for tan undefined sec 2 23) Determine the amplitude of each: 1 f ( x) sin x 4 g ( x) 5cos x h( x) 7 tan x 24) Determine the period of each: f ( x) 2sin 4( x ) g ( x) cos 3 x 1 2 h( x) cot x 3 3 2 25) Determine the phase shift of each: f ( x) 2 cot 4( x ) 26) Graph y 2 cos x 1 2 g ( x) sec 3 x 1 2 h( x) sin x 3 3 2 1 27) Graph y tan 2 x 3 2 29) Find the exact value of each: 1 arcsin 2 2 cos 1 2 tan 1 0 28) Graph y sin 2( x ) 30) Find the exact value of each: sec 1 2 cot 1 1 arc csc 2 32) Find the exact value of arcsin tan 2 33) Graph y = 2 arcsin (2x) 34) Graph y cos1 x 35) A television camera at ground level is filming the lift-off of a space shuttle at a point 750 meters from the launch pad. Find the angle of elevation to the shuttle when it is 1200 meters high. sin cos 36) Simplify sin x cot x cos x 37) Simplify 1 cos sin 2 2 38) Simplify cos x sec x 1 39) Simplify cot sec 31) Find the exact value of tan(arcos ½ ) 40) Solve for all solutions 0 < x < 2 csc2 x cot x 3 0 cos x 42) Verify graphically sec x tan x 1 sin x 44) Solve 2cos x + 1 = 0 46) Use the sum/difference formulas to find the exact value of sin 12 48) Find the exact value of sin 420 cos120 sin120 cos 420 5 3 , 2 then 13 2 find sin , cos 2, and tan 2 50) If cos 52) Solve the triangle if: C 102.30 , B 28.70 , b 27.4 41) Solve for all solutions 0 < x < 2 sec2 x 1 0 43) How many solutions are there for: cos 2 x(2 cos x 1) 0 45) Solve sin3x = sin x 47) Use the sum/difference formulas to find the exact value of tan 750 49) Find the exact value of 3 3 cos cos sin sin 16 16 16 16 51) Use the half-angle formula to find the exact value of sin 105o. 53) Solve the triangle if: A 420 , a 22, b 12 54) How many triangles are possible? 55) How many triangles are possible? 0 A 85 , a 15, b 25 A 20.50 , a 12, b 31 56) Because of Hurricane Ike, a tree grew so that it was leaning 4o from the vertical. At a point 35 meters from the tree, the angle of elevation to the top of the tree is 23o. Find the height of the tree. 0 57) Solve the triangle A 115 , c 10, b 15 58) Solve the triangle c 60, a 80, b 139 59) Find the area of the triangle if: 60) Find the area of the triangle if: a 5, b 7, c 10 A 500 , c 2, b 4 60) Convert 2 2i 3 using cis notation 61) Convert 24 cis 300o. 62) Find the product of 2 11 2cis 3 8cis 6 63) Find the quotient of 4cis500 2cis 200 64) Identify the type of polar graph: r 2 9sin 2 65) Identify the type of polar graph: r 1 2cos 66) How many petals are on the rose: 67) How many petals are on the rose: r = 4 cos 3 r = 3 cos 4 68) State 3 equivalent polar coordinates to (4, 105o). 69) Express in Complex Polar Form: 2 3 - 2 3i 70) Express your answer in rectangular form for: æ 3p 3p ö æ 7p 7p ö 4 ç cos + isin ÷ ·5ç cos + isin ÷ 12 12 ø è 12 12 ø è æ 11p 11p ö 10 ç cos + isin 18 18 ÷ø è 71) Express your answers in rectangular form for æ p pö 5 ç cos + isin ÷ 9 9ø è 8 æ p pö 72)Use DeMoivre’s Theorem to calculate ç cos + isin ÷ and express your answer in the polar 12 12 ø è form 73) Find the magnitude v and direction angle for v = 5,-2 74) Determine if the vectors are parallel, orthogonal or neither: u = 6i +10 j v = 3i - 5 j 75) If u = -1,5 and v = -3,6 find 2u – 5v. 76) Initial point P (5, 2) and terminal point Q (-3, 7) are given, find the resultant vector. 77) If the angle measure between 2 forces is 1000 and one force is 50 pounds and the other is 72 pounds, find the resultant force.