Math Problem Statement
Find the reference angle for a rotation of start fraction, 13, pi, divided by, 7, end fraction 7 13π .
Solution
To find the reference angle for the rotation of , follow these steps:
Step 1: Understand the concept of reference angles.
The reference angle is the smallest positive acute angle that the terminal side of the given angle makes with the x-axis. For angles measured in radians, the reference angle depends on which quadrant the terminal side lies in.
Step 2: Reduce the angle to an equivalent angle between and .
Given , the first thing is to reduce it within the interval .
- Since , subtract from to find the coterminal angle:
- A negative angle implies clockwise rotation, so add to bring it into the positive interval: Thus, the equivalent angle is .
Step 3: Identify the quadrant and find the reference angle.
The reduced angle is in the first quadrant, so it is already the reference angle.
Final Answer: The reference angle is .
Would you like more details or clarifications? Here are some related questions:
- How do you convert between radians and degrees?
- What is the significance of reference angles in trigonometry?
- How do you find the reference angle for angles in the second, third, and fourth quadrants?
- How do coterminal angles help in determining reference angles?
- How can negative angles be interpreted geometrically?
Tip: To quickly reduce any angle larger than (or ), subtract multiples of (or ) to find a coterminal angle.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Radians
Reference Angle
Coterminal Angles
Formulas
Reference angle formula
Coterminal angles formula: θ - 2π or θ + 2π
Theorems
Reference Angle Theorem
Coterminal Angle Theorem
Suitable Grade Level
Grades 10-12