How To Find The Reference Angle In Radians and Degrees - Trigonometry

TL;DR

Reference angles are the angles between the x-axis and the terminal side, and can be easily found using formulas or graphical representations.

Transcript

now let's talk about reference angles and how to find them so let's say if we have an angle of 120 degrees what is the reference angle so let's draw 120 degrees 120 is in quadrant two so this is 120 relative to the positive x-axis the reference angle is the angle between the x-axis and the terminal side or the terminal array and it's always less th... Read More

Key Insights

• 🔺 Reference angles are the angles between the x-axis and the terminal side of an angle.
• 🔺 Reference angles are always less than 90 degrees and can be found using formulas or graphical representations.
• ⚾ Formulas differ based on the quadrant in which the angle is located.
• 🔺 Negative angles can be converted to positive coterminal angles to find the reference angle.
• 🔺 Common angles in the unit circle have specific reference angles.
• 🔺 Reference angles in radians can be found by converting to degrees and using the same formulas.

Questions & Answers

Q: What is a reference angle?

A reference angle is the angle between the x-axis and the terminal side of an angle, always less than 90 degrees.

Q: How can reference angles be found using formulas?

If the angle is in quadrant one, the reference angle is equal to the angle itself. In quadrant two, the reference angle is given by 180 minus the angle. In quadrant three, the reference angle is the angle in quadrant three minus 180. In quadrant four, the reference angle is 360 minus the angle.

Q: How can reference angles be found graphically?

Reference angles can be found by drawing a triangle with the terminal side and the x-axis. The reference angle is the angle formed in the triangle.

Q: How can reference angles be found for negative angles?

To find the reference angle for a negative angle, find the coterminal angle (adding 360 to the negative angle) and then use the formulas explained earlier based on the quadrant in which the coterminal angle is located.

Summary & Key Takeaways

• Reference angles are the angles between the x-axis and the terminal side of an angle, always less than 90 degrees.

• There are formulas to find reference angles based on the quadrant in which the angle is located.

• Reference angles can be found graphically by visualizing the angle and the x-axis in a triangle.