https://file.aiquickdraw.com/mathbot/file/1726053660360xvrsplri.jpg

The problem you provided asks to find all angles that are coterminal with the given angle, -50°, and to express the general solution using \( k \) as an arbitrary integer.

### Coterminal Angles:
Coterminal angles are angles that differ from each other by a multiple of 360°. To find all angles coterminal with -50°, we use the formula:

\[
\theta = -50^\circ + 360^\circ \cdot k
\]

Where \( k \) is any integer (positive, negative, or zero). This gives all the possible angles that are coterminal with -50°.

### Example values for \( k \):
- For \( k = 0 \), the coterminal angle is \( -50^\circ \).
- For \( k = 1 \), the coterminal angle is \( -50^\circ + 360^\circ = 310^\circ \).
- For \( k = -1 \), the coterminal angle is \( -50^\circ - 360^\circ = -410^\circ \).

Thus, the general solution for all coterminal angles is:

\[
\theta = -50^\circ + 360^\circ \cdot k
\]

Would you like more examples or a detailed explanation? Feel free to ask for clarification.

### Related Questions:
1. What are coterminal angles for \( 120^\circ \)?
2. How do you determine if two angles are coterminal?
3. What is the smallest positive coterminal angle to \( -50^\circ \)?
4. Can coterminal angles be fractions of degrees?
5. What are coterminal angles in radians?

**Tip:** When solving for coterminal angles, remember to adjust for negative or large positive values by adding or subtracting \( 360^\circ \) until the angle is between \( 0^\circ \) and \( 360^\circ \).

Find all angles that are coterminal with the given angle. (Let k be an arbitrary integer.) -50°

Explore how to find all angles coterminal with -50° using the formula θ = -50° + 360° * k, where k is an integer. This concept is essential in trigonometry for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation