In the previous lesson, we saw that (cosθ,sinθ) are the coordinates of a point on the unit circle whose angle to the x-axis is θ:
If we trace the values of sinθ and cosθ with θ on the x-axis, we find their sinusoidal graphs:
Notice that both sinx and cosx have a domain of x∈R and a range of (−1,1).
A sinusoidal function is a generalization of sin and cos to the form
or
The tan function is defined by tanx=cosxsinx.
The domain is thus x=22k+1π (there are vertical asymptotes at those x′s), and the range is all real numbers R.
The function has roots at x=0,±π,±2π… (ie x=kπ where k∈Z)
Nice work completing Sinusoidal functions, here's a quick recap of what we covered:
Exercises checked off
In the previous lesson, we saw that (cosθ,sinθ) are the coordinates of a point on the unit circle whose angle to the x-axis is θ:
If we trace the values of sinθ and cosθ with θ on the x-axis, we find their sinusoidal graphs:
Notice that both sinx and cosx have a domain of x∈R and a range of (−1,1).
A sinusoidal function is a generalization of sin and cos to the form
or
The tan function is defined by tanx=cosxsinx.
The domain is thus x=22k+1π (there are vertical asymptotes at those x′s), and the range is all real numbers R.
The function has roots at x=0,±π,±2π… (ie x=kπ where k∈Z)
Nice work completing Sinusoidal functions, here's a quick recap of what we covered:
Exercises checked off