Math Problem Statement

For each of the following terminal arms, determine the angle in standard position, the reference angle, and the angle of a coterminal arm.

Solution

This image shows a circle with an angle labeled as 297-297^\circ, and it's asking for the angle in standard position, the reference angle, and the angle of a coterminal arm.

  1. Angle in standard position: The angle is already in standard position, as it is measured counterclockwise from the positive x-axis. The negative sign indicates that the angle is measured clockwise from the x-axis. So, the angle in standard position remains 297-297^\circ.

  2. Reference angle: The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. For negative angles, we find the reference angle by adding 360° to the given angle and then subtracting it from 360° to get the smallest positive angle.

Reference Angle=360297=63\text{Reference Angle} = 360^\circ - 297^\circ = 63^\circ

  1. Coterminal angle: Coterminal angles are angles that share the same terminal side. To find a coterminal angle, we add or subtract multiples of 360° to the original angle until we get an angle between 0° and 360°.

Coterminal angle=297+360=63\text{Coterminal angle} = -297^\circ + 360^\circ = 63^\circ

So, the coterminal angle is 6363^\circ.

Would you like further details or help with other parts of the problem?


Here are some related questions:

  1. How do you find the reference angle for positive angles?
  2. What is the significance of coterminal angles in trigonometry?
  3. How can you determine the quadrant of a given angle in standard position?
  4. How do you handle angles greater than 360° when finding reference angles?
  5. Can you calculate reference angles for non-standard angles, like radians?

Tip: Remember that reference angles are always positive and acute (less than 90°), regardless of whether the original angle is positive or negative.

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Math Problem Analysis

Mathematical Concepts

Angles
Standard Position of Angles
Reference Angle
Coterminal Angles
Trigonometry

Formulas

Reference Angle = 360° - |angle|
Coterminal Angle = angle ± 360°n (where n is an integer)

Theorems

Properties of Coterminal Angles
Reference Angle Theorem

Suitable Grade Level

Grades 9-12