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Chapter 5: Problem 6

Verify that the \(x\) -values are solutions of the equation. \(\sec x-2=0\) (a) \(x=\frac{\pi}{3}\) (b) \(x=\frac{5 \pi}{3}\)

Short Answer

Expert verified
Yes, both values \(x=\frac{\pi}{3}\) and \(x=\frac{5\pi}{3}\) are verified solutions of the equation \(\sec x-2=0\).

Step by step solution

01

Verifying solution for part a

Firstly, evaluate the given equation for \(x=\frac{\pi}{3}\). The secant of \(\frac{\pi}{3}\) is equal to 2, i.e., \(sec(\frac{\pi}{3})=2\). So if we substitute this value in the equation, we get 2-2 = 0. As this is the same as the right hand side of the given equation, thus \(x=\frac{\pi}{3}\) is a solution of the equation.
02

Verifying solution for part b

Now, evaluate the given equation for \(x=\frac{5\pi}{3}\). The secant of \(\frac{5\pi}{3}\) is equal to 2, i.e., \(sec(\frac{5\pi}{3})=2\). So if we substitute this value in the equation, we get 2-2 = 0. As this is the same as the right hand side of the given equation, thus \(x=\frac{5\pi}{3}\) is also a solution of the equation.

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Most popular questions from this chapter

The monthly sales \(S\) (in thousands of units) of a seasonal product are approximated by $$S=74.50+43.75 \sin \frac{\pi t}{6}$$ where \(t\) is the time (in months), with \(t=1\) corresponding to January. Determine the months in which sales exceed 100,000 units.

Write the expression as the sine, cosine, or tangent of an angle. $$\cos 3 x \cos 2 y+\sin 3 x \sin 2 y$$

Find the exact values of the sine, cosine, and tangent of the angle. $$\frac{13 \pi}{12}$$

Find the exact values of the sine, cosine, and tangent of the angle. $$\frac{5 \pi}{12}$$

Use inverse functions where needed to find all solutions of the equation in the interval \([0,2 \pi)\). $$\csc ^{2} x-5 \csc x=0$$
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