**SA-1** The small angle approximation states that if $\theta \ll 1$ radian, then $\sin(\theta) \approx \theta$, where $\theta$ is in radians. Recall that the percentage error in using this approximation is given by:\[\% \text{ error} = \frac{\text{approximate} - \text{exact}}{\text{exact}} \times 100\]__(a)__ What is the percentage error in using the small angle approximation for the sine function, for an angle of 1 degree?__(b)__ What is the percentage error in using the small angle approximation for the sine function, for an angle of 30 degrees?__(c)__ What is the percentage error in using the small angle approximation for the sine function, for an angle of 80 degrees?

We are given the approximation for sine of an angle. If angle is less than 1 radian, sinθ≈θ We also…

SA-1 The small angle approximation says that if 0 < 1 rad, then sin(0) ≈ 0, where is in radians. Recall that the % error in using this approximation is given by: approximate - exact % error = x 100 exact (a) What is the % error in using the small angle approximation for the sine function, for an angle of 1 degree? (b) What is the % error in using the small angle approximation for the sine function, for an angle of 30 degrees? (c) What is the % error in using the small angle approximation for the sine function, for an angle of 80 degrees?

SA-1 The small angle approximation says that if 0 < 1 rad, then sin(0) ≈ 0, where is in radians. Recall that the % error in using this approximation is given by: approximate - exact % error = x 100 exact (a) What is the % error in using the small angle approximation for the sine function, for an angle of 1 degree? (b) What is the % error in using the small angle approximation for the sine function, for an angle of 30 degrees? (c) What is the % error in using the small angle approximation for the sine function, for an angle of 80 degrees?

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Question

**SA-1** The small angle approximation states that if $\theta \ll 1$ radian, then $\sin(\theta) \approx \theta$, where $\theta$ is in radians. Recall that the percentage error in using this approximation is given by:

\[
\% \text{ error} = \frac{\text{approximate} - \text{exact}}{\text{exact}} \times 100
\]

__(a)__ What is the percentage error in using the small angle approximation for the sine function, for an angle of 1 degree?

__(b)__ What is the percentage error in using the small angle approximation for the sine function, for an angle of 30 degrees?

__(c)__ What is the percentage error in using the small angle approximation for the sine function, for an angle of 80 degrees?

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