Find theta **Finding the Value of θ Without a Calculator**To solve the following trigonometric equation:\[ -2\cos(2θ) = 2 + \cos(2θ) \]You can use trigonometric identities and simplification.### Provided Equations and Identities:1. Double Angle Formulas: \[ \cos\left(\frac{\alpha}{2}\right) = \sqrt{\frac{1 + \cos{\alpha}}{2}} \] \[ \sin\left(\frac{\alpha}{2}\right) = \sqrt{\frac{1 - \cos{\alpha}}{2}} \]### Steps to Solve:1. Simplify the given equation: \[ -2\cos(2θ) = 2 + \cos(2θ) \]2. Move all terms to one side to combine like terms: \[ -2\cos(2θ) - \cos(2θ) = 2 \] \[ -3\cos(2θ) = 2 \]3. Solve for \(\cos(2θ)\): \[ \cos(2θ) = -\frac{2}{3} \]4. Find \(θ\) without using a calculator, utilize the related trigonometric identities. Refer to trigonometric tables or derived values from known angles as part of the solution. These identities simplify the process of solving for \(θ\) based on the values you know or have encountered in trigonometric proofs.The equation above can be further worked out to find approximate or exact values of \(θ\) under different conditions, examining the unit circle, quadrants, and symmetrical properties of trigonometric functions.

Name: Find theta **Finding the Value of θ Without a Calculator**To solve the
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: Find theta **Finding the Value of θ Without a Calculator**To solve the following trigonometric equation:\[ -2\cos(2θ) = 2 + \cos(2θ) \]You can use trigonometric identities and simplification.### Provided Equations and Identities:1. Double Angle Formu