Precalculus Chapter 6 Worksheet Graphing Sinusoidal Functions in ...

Precalculus Chapter 6 Worksheet
Graphing Sinusoidal Functions in Degree Mode
Find the amplitude, period, phase (horizontal) displacement and translation (vertical displacement).
Then use the information to find the critical points and sketch two cycles for the graph (one to the right
and one to the left of the center point).
1. y = 7 + 4cos3( θ − 10 ° )
Amplitude:
Period:
Phase:
Translation:
_________
_________
_________
_________
2. y = − 10 + 20sin 2( θ + 30 ° )
3.
4.
Amplitude:
Period:
Phase:
Translation:
1
y = 3− 5cos ( θ + 90 ° )
2
Amplitude:
Period:
Phase:
Translation:
_________
_________
_________
_________
_________
_________
_________
_________
1
1000 + 3000sin ( 60 )
3 θ + °
Amplitude:
Period:
Phase:
Translation:
5. y = 11− 6sin( θ − 17 ° )
_________
_________
_________
_________
Amplitude:
Period:
Phase:
Translation:
_________
_________
_________
_________

Precalculus Chapter 6 Worksheet
Graphing Sinusoidal Functions in Radian Mode
Find the amplitude, period, phase (horizontal) displacement and translation (vertical displacement).
Then use the information to find the critical points and sketch two cycles for the graph (one to the right
and one to the left of the center point).
1.
2.
1
y = 3+ 2cos ( x − π )
5
Amplitude:
Period:
Phase:
Translation:
_________
_________
_________
_________
2 π
y = − 4 + 5sin x
+ 3 2
Amplitude:
Period:
Phase:
Translation:
_________
_________
_________
_________
π
3. y = 2 − 6cos3x
+
6
Amplitude:
Period:
Phase:
Translation:
π
4. 2 + 6sin ( 1)
4 x −
Amplitude:
Period:
Phase:
Translation:
_________
_________
_________
_________
_________
_________
_________
_________
π
5. y = −5 − 4sin ( x + 2)
3
Amplitude:
Period:
Phase:
Translation:
_________
_________
_________
_________

Graphing Tangent and Reciprocal Functions
Graph the following:
Assume the function is circular (use radians) if the independent variable is x and trigonometric (use
degrees) if the independent variable is θ. Graph two cycle of each.
1. y = tan 2θ
9. y = 4 + 3tanπ
x
π
2. y = cot x 3
10. y = − 5 + 3cot 4θ
π
3. y = csc x 2
11. y = − 6 + 2csc5θ
4. y = sec3θ
π
12. y = 1+
4sec x 10
5. y = 2cot x
13. y = − 1+ 3cot 2( θ − 30 ° )
6.
1
y = tan θ
2
π
14. y = 2 + 5tan ( x − 3)
8
7.
1
y = sec θ
3
π
15. y = 4 + 6sec ( x + 1)
2
8. y = 2cscθ
16. − 3+ 2csc 4( θ + 10 ° )

Precalculus Worksheet
Section 6.8
Find the principal value to 2 decimal places for θ, or 4 decimal places for x.
1.
2.
3.
4.
−
θ = Sin
1 0.195
−
θ = Cos
1 ( − 0.2843)
x = Cos −1 0.845
x = Sin −1 ( − 0.97)
Find the principal value to 2 decimal places for θ, or 4 decimal places for x, getting the general solution
and the first three positive values of θ and x.
5.
6.
7.
8.
9.
10.
11.
12.
θ =
θ =
−1
cos 0.91
−1
sin 0.53
θ = −
−1
cos ( 0.15)
θ = −
x =
x =
−1
sin ( 0.16)
−1
cos 0.26
−1
sin 0.98
x = −
−1
cos ( 0.11)
x = −
−1
sin ( 0.63)
Find the exact principal value of θ and x.
13. θ = Cos
2
−1 1
14. θ = Sin −
2
1 2
15. x = Sin
−
2
1 1
16. x = Cos −
−
2
−1 3
17.
x = Cos −1 5 (Surprise?!)
−
18. θ = Sin
1 ( − 3) (Surprise!!?)