Question

Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0, 21).Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution."2cos(x) - V2 = 0

Answer 1

First we can solve for cos(x):

$\begin{gathered} 2\cos (x)-\sqrt[]{2}=0 \\ \cos (x)=\frac{\sqrt[]{2}}{2} \end{gathered}$

This a very familiar value of cosine. This is the value of cos function when x = pi/4 and x = 7/4 pi

This are the only two values of the function between [0, 2pi) that satifies the equation.

Thus, the solutions are:

$x=\frac{\pi}{4},\frac{7}{4}\pi$