| 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
| i) 120º a)Q 2, b) 2o/3 |
ii) 405º a) Q 1, b) 9o/4 |
iii) 225º a) Q 3, b) 5o/4 |
iv) 375º a) Q 1, b) 25o/12 |
v) -150º a) Q 3, b) -5o/6 |
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3) For the angles listed
| i) 3o/4 a)Q 2, b) 135º |
ii) 2o /5 a)Q 1, b) 72º |
iii) 17o/3 a)Q 4, b) 1020º |
iv) -15o a)x-axis, b)-2700º |
v) -5o/6 a)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
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b) cot A > 0, sin A > 0 d Q 1
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| c) cos A > 0, tan A < 0 d Q 4
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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) - 4 y = 3 sin 4(x + o/4) - 4
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b) y = - 7 cos (3x - 2o) + 2 y = - 7 cos 3(x - 2o/3) + 2
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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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