Find all solutions to the equation. 2 cosx- sinx= 1 Write your answer in radians in terms of t, and use the "or" button as necessary. TC TC +2kn, keZ or x = +kt, keZ 7 Help with Example: x =- %3D this notation

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
Question
**Find all solutions to the equation:**

\[ 2\cos^2{x} - \sin{x} = 1 \]

Write your answer in radians in terms of \(\pi\), and use the "or" button as necessary.

**Example:**

\[ x = \frac{\pi}{5} + 2k\pi, \, k \in \mathbb{Z} \quad \text{or} \quad x = \frac{\pi}{7} + k\pi, \, k \in \mathbb{Z} \]

**Help with this notation**

**Input box for the solution:**
\[ x = \boxed{} \]

Adjacent to the input box, there is a keypad with the following symbols and functionalities:

1. Symbol for \(\pi\)
2. Symbol for \(k\pi, k \in \mathbb{Z}\)
3. "or" button
4. Buttons to confirm (\(\checkmark\)), delete (\(\times\)), and revert changes (\(\circlearrowleft\))
5. Help button (?) for further clarification on the input format

This layout assists students in formatting their answers correctly according to standard mathematical notation.
Transcribed Image Text:**Find all solutions to the equation:** \[ 2\cos^2{x} - \sin{x} = 1 \] Write your answer in radians in terms of \(\pi\), and use the "or" button as necessary. **Example:** \[ x = \frac{\pi}{5} + 2k\pi, \, k \in \mathbb{Z} \quad \text{or} \quad x = \frac{\pi}{7} + k\pi, \, k \in \mathbb{Z} \] **Help with this notation** **Input box for the solution:** \[ x = \boxed{} \] Adjacent to the input box, there is a keypad with the following symbols and functionalities: 1. Symbol for \(\pi\) 2. Symbol for \(k\pi, k \in \mathbb{Z}\) 3. "or" button 4. Buttons to confirm (\(\checkmark\)), delete (\(\times\)), and revert changes (\(\circlearrowleft\)) 5. Help button (?) for further clarification on the input format This layout assists students in formatting their answers correctly according to standard mathematical notation.
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