MATH 108 Summer 2017 Quiz 1 Find the acute angle , to the nearest hundredth of a degree, for the given function value. 1) sin = 0.6131 Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. No decimal answers. 2) cos , if sec = -4 3) Find sin 2 if cos = 2/3 and is in quadrant IV. 4) Find cot if tan = 7 3 and is in quadrant III. Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. 5) Find sin A and tan A. A 4 6 Without using a calculator, give the exact trigonometric function values with rational denominators. 6) tan 60 7) sin 45 8) sec 270 Find the exact circular function value. 9) cos 2/3 10) tan 5/6 Find the trigonometric function value of angle . 11) sin = - 5/13 and in quadrant III Find sec and csc 12) cot = - and in quadrant II Find csc and sin Solve the problem. 13) What radius corresponds to an arc length of 8 ft and a central angle of 35 ? Round to the nearest hundredth of a foot. 14) What arc length corresponds to a radius of 9.5 cm and a central angle of nearest hundredth of a cm 5 12 ? Round to the Find the acute angle , to the nearest hundredth of a degree, for the given function value. 1) sin = 0.6131 tak e inverse sin of bothsides =sin1 (0.6131)=37.81 Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. No decimal answers. 2) cos , if sec = -4 sec ( ) = 1 =4 cos ( ) cos ( ) = 1 4 3) Find sin 2 if cos = 2/3 and is in quadrant IV. We know that 2 2 cos ( x )+ sin ( x )=1 then 2 2 2 2 5 =1 = 3 3 9 () sin 2 ()1cos 2 ( )=1 () Take square root of both sides 1 5 2 5 sin ( )= = 9 3 () In Quadrant Iv, Sin is negative thensin ( 2 )=2 sin ( ) cos ( )=2 4) Find cot if tan = cot ( )= 7 3 (3 5 )( 23 )=495 and is in quadrant III. 1 1 3 7 = = 7 tan ( ) 7 3 Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. 5) Find sin A and tan A. A 4 6 we first find the hypotenuse x= ( 4 +6 ) 2 2 x=7.2 Sine: sin() = Opposite / Hypotenuse = 6 7.2 Tangent: tan() = Opposite / Adjacent =6/4 Without using a calculator, give the exact trigonometric function values with rational denominators. 6) tan 60 tan ( 60 ) =3 7) sin 45 sin ( 45 ) = 1 2 8) sec 270 sec ( 270 )= Find the exact circular function value. 9) cos 2/3 2 1 cos = 3 2 ( ) 10) tan 5/6 5 1 tan = 6 3 ( ) Find the trigonometric function value of angle . 11) sin = - 5/13 and in quadrant III Find sec and csc Sine: sin() = Opposite / Hypotenuse 5 O pposite sin ( )= = 13 H ypotenuse x= 13252 now we find adj be 12 sec ( ) = H ypotenuse 13 = adj 12 sin ( 1 13 csc ( )= = 5 12) cot = - and in quadrant II Find csc and sin 1 opposite 3 cot ( )= = = adj 4 tan ( ) So we find H ypotenuse= 3 +4 =5 2 2 Sine: sin() = Opposite / Hypotenuse 3 5 sin ( 1 5 csc ( )= = 3 Solve the problem. 13) What radius corresponds to an arc length of 8 ft and a central angle of 35 ? Round to the nearest hundredth of a foot. First we convert 35 degrees to radians S=r Formula we are looking for r S 8 288 r= = = 7 7 36 14) What arc length corresponds to a radius of 9.5 cm and a central angle of hundredth of a cm S=r Formula 5 12 ? Round to the nearest s= 5 95 ft 9.5= 12 24 cm MATH 108 Summer 2017 Quiz 2 Simplify the expression completely. 3 1) 21 cos x sinx 2 7 sin x cosx 2) 4 7 + 2 cos x sin x cosx+ sinx 3) 10 tan 3 x 5tanx secx sec 2 x 4) cos2 x 2cos x8 cos x4 2 Graph. 5) y = sin(x + 3/2) Find the amplitude, period or phase shift. 6) Find the period and phase shift of y = 2 cos ( 14 x + 3 ) . 7) Find the amplitude of y = 5 cos (x - ). 8) Find the period of y = 2 cos (2x + /3). 9) Find the phase shift of y = -4 + 3sin (5x - /6) 10) Find 11) Find s 1 ( 1 ) 2 exactly in degrees. 1 tan ( 3) exactly in radians. 12) A person is watching a car from the top of a building. The car is traveling on a straight road directly toward the building. When first noticed the angle of depression to the car is 28.45. When the car stops, the angle of depression is 43.25. The building is 270 feet tall. How far did the car travel from when it was first noticed until it stopped? Round your answer to the hundredths place. 13) In one area, the lowest angle of elevation of the sun in winter is 27.35. Find the minimum distance x that a plant needing full sun can be placed from a fence that is 5.7 feet high. Round your answer to the tenths place. Find the acute angle , to the nearest hundredth of a degree, for the given function value. 1) sin = 0.6131 tak e inverse sin of bothsides =sin1 (0.6131)=37.81 Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. No decimal answers. 2) cos , if sec = -4 sec ( ) = 1 =4 cos ( ) cos ( ) = 1 4 3) Find sin 2 if cos = 2/3 and is in quadrant IV. We know that 2 2 cos ( x )+ sin ( x )=1 then 2 2 2 2 5 =1 = 3 3 9 () sin 2 ()1cos 2 ( )=1 () Take square root of both sides 1 5 2 5 sin ( )= = 9 3 () In Quadrant Iv, Sin is negative thensin ( 2 )=2 sin ( ) cos ( )=2 4) Find cot if tan = cot ( )= 7 3 (3 5 )( 23 )=495 and is in quadrant III. 1 1 3 7 = = 7 tan ( ) 7 3 Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. 5) Find sin A and tan A. A 4 6 we first find the hypotenuse x= ( 4 +6 ) 2 2 x=7.2 Sine: sin() = Opposite / Hypotenuse = 6 7.2 Tangent: tan() = Opposite / Adjacent =6/4 Without using a calculator, give the exact trigonometric function values with rational denominators. 6) tan 60 tan ( 60 ) =3 7) sin 45 sin ( 45 ) = 1 2 8) sec 270 sec ( 270 )= Find the exact circular function value. 9) cos 2/3 2 1 cos = 3 2 ( ) 10) tan 5/6 5 1 tan = 6 3 ( ) Find the trigonometric function value of angle . 11) sin = - 5/13 and in quadrant III Find sec and csc Sine: sin() = Opposite / Hypotenuse 5 O pposite sin ( )= = 13 H ypotenuse x= 13252 now we find adj be 12 sec ( ) = H ypotenuse 13 = adj 12 sin ( 1 13 csc ( )= = 5 12) cot = - and in quadrant II Find csc and sin 1 opposite 3 cot ( )= = = adj 4 tan ( ) So we find H ypotenuse= 3 +4 =5 2 2 Sine: sin() = Opposite / Hypotenuse 3 5 sin ( 1 5 csc ( )= = 3 Solve the problem. 13) What radius corresponds to an arc length of 8 ft and a central angle of 35 ? Round to the nearest hundredth of a foot. First we convert 35 degrees to radians S=r Formula we are looking for r S 8 288 r= = = 7 7 36 14) What arc length corresponds to a radius of 9.5 cm and a central angle of hundredth of a cm S=r Formula 5 12 ? Round to the nearest s= 5 95 ft 9.5= 12 24 cm MATH 108 Summer 2017 Quiz 2 Simplify the expression completely. 3 1) 21 cos x sinx 2 7 sin x cosx 2) 4 7 + 2 cos x sin x cosx+ sinx 3) 10 tan 3 x 5tanx secx sec 2 x 4) cos2 x 2cos x8 cos x4 2 Graph. 5) y = sin(x + 3/2) Find the amplitude, period or phase shift. 6) Find the period and phase shift of y = 2 cos ( 14 x + 3 ) . 7) Find the amplitude of y = 5 cos (x - ). 8) Find the period of y = 2 cos (2x + /3). 9) Find the phase shift of y = -4 + 3sin (5x - /6) 10) Find 11) Find s 1 ( 1 ) 2 exactly in degrees. 1 tan ( 3) exactly in radians. 12) A person is watching a car from the top of a building. The car is traveling on a straight road directly toward the building. When first noticed the angle of depression to the car is 28.45. When the car stops, the angle of depression is 43.25. The building is 270 feet tall. How far did the car travel from when it was first noticed until it stopped? Round your answer to the hundredths place. 13) In one area, the lowest angle of elevation of the sun in winter is 27.35. Find the minimum distance x that a plant needing full sun can be placed from a fence that is 5.7 feet high. Round your answer to the tenths place