Math 114
Worksheet for 30 Oct
3.3, 3.4, 4.1
1. Given the point is on a unit circle, complete the ordered pair (x, y) for the quadrant indicated.
• (x, −0.8); QIII
•
5
, y ; QIV
13
2. Verify the point given is on a unit circle, then use symmetry to find three more points on the
circle.
!
√
3 1
,
• −
2 2
√
•
7 3
,−
4
4
!
3. Without the use of a calculator, state the exact value of the trig functions for the given angle.
A diagram will help.
π • sin
4
7π
• sin −
4
3π
2
5π
4
7π
3
• cos
• cos
• tan
• tan (0)
• sec (−π)
1
4. Without using a calculator, find the two values of θ in [0, 2π) that make each equation true.
√
• sec θ = − 2
2
• csc θ = − √
3
• tan θ = undefined
• csc θ = undefined
√
• sin θ =
2
2
• sin θ = 0
• cos θ = −1 (only one answer)
5. Clearly state the amplitude and period of each function, then match it with the corresponding
graph in Figure 1.
• y = −2 cos(4t)
• y = 2 sin(4t)
• y = 3 sin(2t)
• y = −3 cos(2t)
• y=
3
4
cos(0.4t)
• y=
7
4
cos(0.8t)
6. The graphs shown in Figure 2. are of the form y = A cos(Bt). Use the characteristics
illustrated for each graph to determine its equation.
2
Figure 1:
Figure 2:
3