Question

Use trigonometric identities and algebraic methods, as necessary, to solve the following trigonometric equation. Please identify all possible solutions by including allanswers in [0, 2x) and indicating the remaining answers by using n to represent any integer. Round your answer to four decimal places, if necessary. If there is nosolution, indicate "No Solution."272cos(x) + 2 = 0

Answer 1

Given the trigonometric equation:

2√2 cos (x) + 2 = 0

We can rewrite it, as:

2√2 cos (x) = - 2

Dividing both sides by two:

√2 cos (x) = - 1

Rationalizing:

cos (x) = - √2/2

Solving for cos(x):

`\begin{gathered} x\text{ = }(3\pi)/(4) \\ \\ x\text{ = }(5\pi)/(4) \end{gathered}`