MATH 536 TRIG QUIZ SOLUTIONS

1)Complete the following table without a calculator: do not rationalize!!

you are allowed to copy and paste the table so you can print it out for effeciency -- just the table!!

(images of unit circle, 30, 60, 90 and isosceles right triangles for exact values -- click here)

 A sin A cos A tan A csc A sec A cot A -o/6 -1/2 -2 o/2 -1 0 - º -1 º 0 -4o/3 -1/2 -2 3o/4 -1 -1 -3o 0 -1 0 º -1 - º 0 0 -1 0 º 1 º

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2) For the angles listed

a) indicate the quadrant in which the angle is found
b) convert to radian measure. Do not use 3.14 for
o

 i) 120º a)Q 2, b) 2o/3 ii) 405ºa) Q 1, b) 9o/4 iii) 225ºa) Q 3, b) 5o/4 iv) 375ºa) Q 1, b) 25o/12 v) -150ºa) Q 3, b) -5o/6

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3) For the angles listed

a) indicate the quadrant in which the angle is found
b) convert to degree measure.

 i) 3o/4a)Q 2, b) 135º ii) 2o /5a)Q 1, b) 72º iii) 17o/3a)Q 4, b) 1020º iv) -15oa)x-axis, b)-2700º v) -5o/6a)Q 3, b) -150º

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4) List the 5 remaining trig functions for angle A. In which quadrant is angle A?
(make a diagram)

 a) sin A = < 0, cos A > 0 d Q 4 b) cot A > 0, sin A > 0 d Q 1 c) cos A > 0, tan A < 0 d Q 4 d) csc A = -9/5, cot A > 0 d Q 3

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5) Prove these identities

 a) cot x + = csc x b) 2 sin A + tan A = RHS c) (sin A + cos A)2 + (sin A - cos A)2 = 2 LHS sin 2 A + 2 sinA cosA + cos 2 A + sin 2 A - 2 sinA cosA + cos 2 A = sin 2 A + cos 2 A + sin 2 A + cos 2 A = 1 + 1 = 2 = RHS

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6) State the amplitude, period, phase shift, max and min, then graph

 a) y = 3 sin (4x + o) - 4y = 3 sin 4(x + o/4) - 4 amp = 3, period = o/2, h = - o/4, max = -1, min = -7 b) y = - 7 cos (3x - 2o) + 2y = - 7 cos 3(x - 2o/3) + 2 amp = 7, period = 2o/3, h = -2o/3, max = 9, min = -5

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7) Graph one cycle of

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Images for Exact Values

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the unit circle

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