1) Convert 13 32' 47" to decimal degrees. Round your answer to four decimal places.

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1 PRECLCULUS FINL EXM, PRCTICE UNIT ONE TRIGONOMETRIC FUNCTIONS ) Convert ' 47" to decimal degrees. Round your answer to four decimal places. ) Convert to degrees, minutes, and seconds. Round to the nearest second. ) Evaluate: ' 45" 75 ' 56". 4) One angle of a triangle has a measure of 9 9', while another angle of the triangle has measure 8 5'. Find the measure of the third angle. 5) The terminal side of an angle θ in standard position passes through the point ( 4, ). Find the EXCT (no decimals) values of the si trigonometric functions of θ. 6) n angle has a measure of 7. Determine two angles (one positive and one negative) that are coterminal with this angle. UNIT TWO TRIGONOMETRIC FUNCTIONS 7) θ ( θ + ) = ( θ + ) Solve for : sin cos 4. 8) Use a calculator to evaluate csc 8'. Round your answer to four decimal places. 9) Solve the following right triangle, assuming that the right angle is at C. Round all answers to one decimal point. a = 4, = 9.8 0) Solve the following right triangle, assuming that the right angle is at C. Round all answers to one decimal point. = 54., c = 76. ) radio technician is at a spot that has an angle of elevation of 8.5 to the top of the 55-foot-tall transmitting antenna. How far is the radio technician from the ase of the transmitting antenna? ) sailoat travels 6 miles on a earing of 48, and then it travels on a earing of 8 for miles. How far is the sailoat from its starting position?

2 UNIT THREE PPLICTIONS OF TRIGONOMETRY & VECTORS ) If C =, =.5, and c= 47.8, solve for a using the Law of Sines. 4) If C = 9., = 5., and a= 4.6, solve for c using the Law of Sines. 5) If =.8, =.6, and a= 5.8, solve for using the Law of Sines. 6) If a= 9, = 49, and c= 6, solve for C using the Law of Cosines. 7) If C = 8., = 5.7, and a= 4., solve for c using the Law of Cosines. 8) Two towers are.9 mi apart. n oserver on tower spots a fire at a earing of N 47. E. n oserver on tower spots the same fire at a earing of N 59.6 W. How far is the fire from each oserver? 9) oat travels at a earing of 9.6 from point for 9.4 miles. The oat then travels for 69.5 miles at a earing of How far is the oat from point? 0) plane is flying at 40 mph at a earing of. wind is lowing due east at a speed of 47 mph. Find the groundspeed of the plane. ) Two forces of 69 newtons and 4 newtons act at a point. The angle etween the two forces is 4. Find the magnitude of the resultant force. UNIT FOUR RDIN MESURE ND CIRCULR FUNCTIONS ) Convert 65 into radians. Leave your answer in terms of. ) Convert 8 radians into degrees. 9 4) Convert. radians into degrees and minutes. Round the answer to the nearest minute. 5) circle has a radius of 9 cm. central angle intercepts an arc with a length of 4 cm. Find the measure of the central angle, measured to the nearest tenth of a degree. 6) Find the length of the arc on a circle of radius 6. cm intercepted y a central angle of 0. Round the answer to one decimal place. 7) Find the area of a sector of a circle intercepted y a central angle of 0 in a circle of radius 8.6 in.

3 8) 9) 0) Use the Unit Circle to give the EXCT value (NO decimals) of cos. 7 Use the Unit Circle to give the EXCT value (NO decimals) of tan. 6 9 Use the Unit Circle to give the EXCT value (NO decimals) of csc. 4 ) Two gears are adjusted so that the smaller gear drives the larger gear. The smaller gear has a radius of 8. cm, while the larger gear has a radius of 7 cm. If the smaller gear rotates through 80, through how many degrees will the larger gear rotate? Round the answer to one decimal place. ) Find the angular velocity (in radians per minute) and the linear velocity (in meters per minute) of a point on the edge of a disc rotating 4 times per minute. The diameter of the disc is.8 meters. UNIT FIVE GRPHS OF THE CIRCULR FUNCTIONS & TRIGONOMETRIC EQUTIONS ) 4) Find the EXCT value (NO decimals) of csc tan. 4 5 Find the EXCT value (NO decimals) of cot arcsin. Solve the equation cos 0 over the interval 0,. 5) θ + = [ ) 6) θ = θ [ ) Solve the equation sec sec over the interval 0,. 7) θ = [ ) Solve the equation 4sin over the interval 0, 60. 8) [ ) Solve the equation cos θ + sin θ + cosθ = over the interval 0, 60. 9) State the amplitude, period, vertical shift, and phase shift of the following equation: y = 4+ sin +

4 40) State the amplitude, period, vertical shift, and phase shift of the following equation: y = 4cos 4) Which of the following est represents the given equation? UNIT SIX TRIGONOMETRIC IDENTITIES 4) Verify the following identity: ( θ) sec cosθ = sinθ tanθ 4) Determine which one of the following is an identity: ) α tan α tan = ) cot sin sin θ θ = θ C) sin = cos sec D) tan sin cos = 44) Determine which one of the following is an identity: ) sin a = cot a sin a ) cotθ secθ = cosθ C) + tan = D) tan cos sec β cos β tan β + cot β = 45) sin θ Use identities to epress in terms of sin θ and cos θ, then simplify. secθ + tanθ

5 46) secθ tanθ Use identities to epress in terms of sin θ and cos θ, then simplify. secθ ************NSWERS************* ) ' 47" = + / / 600 = ) = ( ) = = 0.5' = = 7.5" ' 08" ) ' 45" = 7' 45" = 7' 05" ' 45" 75 ' 56" 7' 05" 75 ' 56" = 46 40' 49" 4) 9 9' + 8 5' = 0 8' = ' s in a triangle add up to ' = 79 60' 79 60' ' = 68 9' 5) r = + y r = 4 + = 6+ 9 = 5 = 5 r = 5 y 4 4 y sin θ = = =, cos θ = = =, tan θ = = =, r 5 5 r r 5 5 r csc θ = = =, sec θ = = =, cotθ = = = y 4 4 y 6) = 497, 7 60 = 7) sin & cos are cofunctions The two given angles must add up to 90 θ + + θ + 4 = 90 5θ + 5 = 90 5θ = 75 θ = 5 8) Convert 8' to decimal degrees 8' = + 8 / 60 =. csc is reciprocal of sin csc. = / sin. = csc 8'.874 9) Find c y using Pythagorean Theorem c c + = = = c c 57.9 tan 4/9.8 tan tan = = = = = = 4.5

6 0) = = 5.7 a cos 54. = a= cos a= a sin 54. = = sin = ) 55 tan8.5 = = 55/ tan8.5 = feet ft ) C = = 90 Use Pythagorean Theorem 6 + = 50 = 50 = = =.8 miles C 48 6 m m ) 4) 5) 6) sin6.5 sin = 80.5 = 6.5 = a 47.8 a = sin sin a = a 7.5 sin 98.6 sin 9. = = 98.6 = 4.6 c c= 4.6 sin 9. sin 98.6 c= c.4 sin.8 sin = sin = sin sin = = sin = = cosc 969 = 4 84 cosc 77 = 84 cosc = cosc C = cos C = C 04.8

7 7) c = cos 8. c = c = c = c.8 8) = = 4.9 = = 0.4 C = = 06.7 sin06.7 sin 4.9 = a a 59.6 a =.9 sin 4.9 sin a = a.8 miles sin06.7 sin m =.9 =.9 sin 0.4 sin06.7 = miles Distance from tower. miles, Distance from tower.8 miles C 9) C = =. = cos. = = = miles 9.4 m m C 0) C = + 90 = = cos = = = mph 47 mph C 40 mph

8 ) C = 80 4 = 56 = cos 56 = = = newtons C 4 n n 4 69 n ) ) 4) 65 = = = = = '. radians = 70 8' 5) s = θ r 4 = θ 9 θ = radians Convert radians to degrees = θ ) 7) 8) 9) 7 7 Convert degrees to radians 0 θ = s = θ r s = s = s.7 cm Convert degrees to radians 0 θ 80 = 8.6 = in = = Convert to mied numer = Sutract = 5 5 Convert to improper fraction = Use Unit Circle cos = cos = ( ) ( ) ( ) ( ) 7 sin 7 /6 sin 7 /6 / tan = Use Unit Circle = 6 cos 7 /6 cos 7 /6 / / 7 = = = tan = / 6 θ r

9 0) 9 9 Convert to mied numer = Keep adding until positive = + = Convert to improper fraction = Use Unit Circle csc = = = = csc = 4 sin 7 /4 / 4 ) Convert 80 to radians 80 = radians Calculate arc length of smaller 80 gear s = θ r s = 8. s = cm Larger gear must travel same arc length s = θ r = θ radians = θ 80 Convert radians to degrees θ = = Larger gear rotates approimately 54.7 θ ) ω = revolution = radians, 4 revolutions = 48 radians t 48 radians ω = ngular velocity ( ω) = 48 radians/minute minute Linear velocity v = ngular velocity ω Radius r v= ω r 48 Diameter of.8 m = Radius of.4 m v=.4 m v= 67. meters/minute v=.506 v. meters/minute ) Draw right triangle with acute angle, opposite side =, adjacent side = 4 Determine hypotenuse using Pythagorean Theorem + 4 = = 5 = Hypotenuse = 5 Hypotenuse 5 5 csc = csc = csc tan Opposite = 4 4 4) Draw right triangle with acute angle, opposite side = 5, hypotenuse = Determine other leg using + = + = Pythagorean Theorem = = 44 Leg djacent 5 cot = cot = cot arcsin Opposite 5 = 5 5

10 5) cos θ+ = 0 cosθ = cosθ = Use Unit Circle to find cosine values equal to cos θ = at and θ = & ) θ θ θ θ θ( θ ) sec = sec sec + sec = 0 sec sec + = 0 secθ = 0 or secθ + = 0 secθ = 0 or secθ = secθ = 0 is impossile secθ = when cos θ =, ecause sec and cos are reciprocals Use Unit Circle 4 4 to find cosine values equal to cos θ = at and θ = & 7) θ = θ = θ = θ =± 4 4 sine values equal to ± sin θ =± at 0, 50, 0, and 0 θ = 0, 50, 0, & 0 4sin sin sin sin Use the Unit Circle to find 8) cos θ sin θ cosθ Replace sin θ with ( cos θ) + + = cos θ + cos θ + cosθ = cos θ + cosθ + = cos θ + cosθ = 0 cosθ cosθ + = 0 cosθ = 0 or cosθ + = 0 cosθ = 0 or cosθ = Use Unit Circle to find cosine values equal to 0 or cosθ = 0 at 90 and 70, cosθ = at 80 θ = 90, 80, & 70 y = c+ asin d a = amplitude, = period, c= vertical translation, d = phase shift y = 4 + sin + a =, =, c= 4, d = mplitude = =, Period = =, Vertical Translation = 4 = 4 units down, / Phase Shift = = = units to the left 9)

11 y = c+ acos d a = amplitude, = period, c= vertical translation, d = phase shift y = 4cos a= 4, =, c=, d = 0 mplitude = 4 = 4, Period = = 4, Vertical Translation = = units up, / 0 Phase Shift = = 0 = No phase shift / 40) 4) y ( ) 4) = sin mplitude = =, Vertical Translation = unit up Graph has amplitude =, vertical translation = 0 Graph has amplitude =, vertical translation = Graph C has amplitude =, vertical translation = 0 Graph D has amplitude =, vertical translation = Correct answer is D sec θ cosθ tan θ cosθ sinθ = = tanθ cosθ = cosθ = sinθ tanθ tanθ cosθ cosθ ) cotθ sin θ = cotθ sinθ cosθ = sinθ cosθ = cos θ = sinθ sin θ = sin θ 4) 44) C) = = = = = tan tan sin / cos cos sin sin cos + tan sec / cos cos 45) 46) sin θ sin θ cos θ sin θ cos cos = = θ = ( sinθ cosθ) θ = secθ + tanθ / cosθ + sin θ/ cosθ + sin θ / cosθ + sinθ sinθ cos θ sinθ sin θ sinθ + sinθ sinθ = = = + sinθ + sinθ + sinθ sinθ sinθ = sinθ sin θ ( θ) secθ tanθ / cosθ sin θ/ cosθ sin /cosθ sinθ cosθ = = = = sinθ secθ / cosθ / cosθ cosθ