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Chapter 4: Problem 90

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is in the correct mode.) $$\csc \left(-\frac{15 \pi}{14}\right)$$

Short Answer

Expert verified
The exact value for \(\csc(-\frac{15 \pi}{14})\) will depend on the value obtained for \(\sin(-\frac{15 \pi}{14})\) on your specific calculator. Then, taking the reciprocal and rounding to four decimal places will yield the final answer.

Step by step solution

01

Set the Calculator to Radian Mode

Make sure your calculator is set to radian mode because the angle provided is in terms of \(\pi\) (pi), a radian measurement.
02

Calculate the Value of the Angle

Calculate the value of the angle \(-\frac{15 \pi}{14}\). This value will provide you the radian measure of the angle.
03

Calculate the Sine

Calculate the sine of the angle \(\sin(-\frac{15 \pi}{14})\). Remember, the cosecant (\(\csc\)) is defined as the reciprocal of the sine function (\(\sin\)).
04

Calculate the Cosecant

Take the reciprocal of the value obtained for the sine in the previous step to get the cosecant (\(\csc\)) of the angle. That is, \(\csc(-\frac{15 \pi}{14}) = \frac{1}{\sin(-\frac{15 \pi}{14})}\).
05

Round the Answer

Round the calculation from the previous step to four decimal places to get the final answer.

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Most popular questions from this chapter

Use a graphing utility to graph the function. Use the graph to determine the behavior of the function as \(x \rightarrow c\) (a) \(x \rightarrow\left(\frac{\pi}{2}\right)^{+}\) (b) \(x \rightarrow\left(\frac{\pi}{2}\right)^{-}\) (c) \(x \rightarrow\left(-\frac{\pi}{2}\right)^{+}\) (d) \(x \rightarrow\left(-\frac{\pi}{2}\right)^{-}\) $$f(x)=\tan x$$

Use a graphing utility to graph the function. $$f(x)=\pi-\sin ^{-1}\left(\frac{2}{3}\right)$$

\(\quad\) A point on the end of a tuning fork moves in simple harmonic motion described by \(d=a \sin \omega t .\) Find \(\omega\) given that the tuning fork for middle C has a frequency of 264 vibrations per second.

Graph the functions \(f\) and \(g .\) Use the graphs to make a conjecture about the relationship between the functions. $$f(x)=\cos ^{2} \frac{\pi x}{2}, \quad g(x)=\frac{1}{2}(1+\cos \pi x)$$

Sketch a graph of the function and compare the graph of \(g\) with the graph of \(f(x)=\arcsin x\). $$g(x)=\arcsin \frac{x}{2}$$
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