Final Exam Review 1 - Scf
Final Exam Review 1 - Scf Final Exam Review 1 - Scf
Graphs of the Trigonometric Functions 17. Find the amplitude, period and phase shift. Then, sketch one complete period of each graph. On your graphs state the exact values for the endpoints, quarter, half and three-quarter points of the period. a) y = 3sin x b) y = 3sin 4x c) y = −cosπx y = 3csc x y = −1+ 3sin 4x y = −secπx ⎛ π ⎞ ⎛ π ⎞ d) y = sin⎜ x − ⎟ e) y = 2cos⎜3x + ⎟ ⎝ 4 ⎠ ⎝ 2 ⎠ 18. Sketch the graph of each equation below. Be sure to state exact values for the asymptotes and xintercept. a) 1 y = tan x 2 b) y = tan 4x 1 y = cot x 2 y = cot 4x
Proving Identities 19. Verify each identity: 2 2 2 2 secθ sinθ a) tan θ cos θ + cot θ sin θ = 1 b) + = 2 tanθ cscθ cosθ 2 2 2 c) sin θ (cscθ − sinθ ) = cos θ d) sec θ − tan θ = 1 1 1 2 e) + = 2csc x 1+ cos x 1− cos x ⎛ π ⎞ ⎛ π ⎞ g) cos ⎜ x + ⎟ + cos⎜ x − ⎟ = 2 cos x ⎝ 4 ⎠ ⎝ 4 ⎠ i) ⎛ 3π ⎞ f) sin⎜ − x⎟ = −cos x ⎝ 2 ⎠ cos 2x h) = cos x − sin x cos x + sin x sin 2θ sin 3x − sin x cotθ = j) = cot 2x 1− cos 2θ cos x − cos3x
- Page 1 and 2: MAC 1114 Review for Final Exam Defi
- Page 3: 12. ⎛ If angle θ is in standard
- Page 7 and 8: Solving Trigonometric Equations 25.
- Page 9 and 10: Law of Cosines 33. In triangle ABC
- Page 11: Roots of a Complex Number 44. Given
Graphs of the Trigonometric Functions<br />
17. Find the amplitude, period and phase shift. Then, sketch one complete period of each graph. On<br />
your graphs state the exact values for the endpoints, quarter, half and three-quarter points of the<br />
period.<br />
a) y = 3sin<br />
x<br />
b) y = 3sin<br />
4x<br />
c) y = −cosπx<br />
y = 3csc<br />
x<br />
y = −1+<br />
3sin<br />
4x<br />
y = −secπx<br />
⎛ π ⎞<br />
⎛ π ⎞<br />
d) y = sin⎜<br />
x − ⎟ e) y = 2cos⎜3x<br />
+ ⎟<br />
⎝ 4 ⎠<br />
⎝ 2 ⎠<br />
18. Sketch the graph of each equation below. Be sure to state exact values for the asymptotes and xintercept.<br />
a)<br />
1<br />
y = tan x<br />
2<br />
b) y = tan 4x<br />
1<br />
y = cot x<br />
2<br />
y =<br />
cot 4x
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