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F30 – Unit 6 – Sinusoidal Functions Name: ____________________________UNIT PRACTICE TEST Date: _____________________________
Unit 6 – Sinusoidal Functions – PRACTICE TEST
1. For the following pair of angle measures, determine which measure is greater. Explain your reasoning. 455°, 6.35
2. You are installing a knob on a shelf and are spinning it on until it is tightened. The knob has to end facing the same direction that it started in. You spin the knob for 2770°. What angle must you tighten the knob at to turn the knob in the right direction? Show your answer as a picture, as an angle, and as a radian.
3. Imagine that it is now 7:15 p.m.a) How many degrees will the minute hand rotate through before noon the next day? What is the equivalent angle in radians?
b) What time will it be when the minute hand has rotated through 5π4 radians?
c) What time will it be when the minute hand has rotated through 732°?
F30 – Unit 6 – Sinusoidal Functions Name: ____________________________UNIT PRACTICE TEST Date: _____________________________
4. Sketch a possible graph of a sinusoidal function with the following set of characteristics. Explain your decision.
Domain: {x | 0 ≤ x ≤ 1050°, x ∈ R}Maximum value: 7Minimum value: –3Period: 200°y-intercept: – 3
x
y
5. The graph of a sinusoidal function is shown. Describe this graph by determining its range, the equation of its midline, its amplitude, and its period. Show your work. (4 marks)
x
1
2
3
4
5
–1
–2
–3
–4
–5
y
30° 60° 90° 120°
F30 – Unit 6 – Sinusoidal Functions Name: ____________________________UNIT PRACTICE TEST Date: _____________________________
6. The graph of a sinusoidal function is shown.
x
1
2
3
4
5
–1
–2
–3
–4
–5
y
a) Determine the period of this graph. Show your work.
b) Determine the y-value of this graph when x = 6. Explain your answer.
c) Determine the y-value of this graph when x = 1.75. Explain your answer.
7. Write an equation for the following graph as a sine and a cosine function.
x
1
2
3
4
5
–1
–2
–3
–4
–5
y
0.5 1.0 1.5 2.0
30° 60° 90° 120°
F30 – Unit 6 – Sinusoidal Functions Name: ____________________________UNIT PRACTICE TEST Date: _____________________________
8. Write an equation for the following graph as a sine and a cosine function .
x
1
2
3
4
5
–1
–2
–3
–4
–5
y
9. Graph the following function and state the amplitude, equation of its midline, range, and period for the domain: {x|0≤x ≤4.4 , x∈R }. Show your work. y = 2 cos 4(x – 1.6) – 3
x
y
0.5 1.0 1.5 2.0
F30 – Unit 6 – Sinusoidal Functions Name: ____________________________UNIT PRACTICE TEST Date: _____________________________
10. Graph the following function and state the amplitude, equation of its midline, range, and period. Show
your work. y = 2 sin 43 (x + 67.5°) – 2
x
y
13. The following data set is sinusoidal. Determine the missing values from the table.
x 4 8 12 16 20 24 28 36 42 60y 124 135 124 113 124 135
F30 – Unit 6 – Sinusoidal Functions Name: ____________________________UNIT PRACTICE TEST Date: _____________________________
F30 – Unit 6 – Sinusoidal Functions Name: ____________________________UNIT PRACTICE TEST Date: _____________________________
F30 – Unit 6 – Sinusoidal Functions Name: ____________________________UNIT PRACTICE TEST Date: _____________________________
F30 – Unit 6 – Sinusoidal Functions Name: ____________________________UNIT PRACTICE TEST Date: _____________________________
F30 – Unit 6 – Sinusoidal Functions Name: ____________________________UNIT PRACTICE TEST Date: _____________________________
