Subtract 360° 360° from 450° 450° . The resulting angle of **90° 90°** is positive, less than 360° 360° and equivalent to 450° 450°.

Contents

- What is the reference angle of 445 degrees?
- What is the reference angle for 405 degrees?
- What is the reference angle of 460 degrees?
- What is the reference angle for 400 degrees?
- What is the reference angle for 455 degrees?
- How do you find a reference angle?
- How do you graph 480 degrees?
- How do you find the value of tan 405?
- How do you find sin 405 without a calculator?
- What is the reference angle of 435?
- What is the reference angle for 570?
- What is the reference angle of 675?
- What is the reference angle for 640 degrees?
- What is the reference angle of 170 degrees?
- How do you find the reference angle of 290 degrees?
- What is the reference angle for 330 degrees?
- What is the reference angle of 240?
- What is the reference angle of 150 degrees?
- What is the reference angle of 180?

Trigonometry Examples

Find an angle that is positive, less than 360° and equal to 445°. Subtract 360° 360° from 445° 445° . The resulting angle of **85° 85°** is positive, less than 360° 360° and equivalent to 445° 445°.

Explanation: On the unit circle, the nearest x-axis to 405 degrees is 360 degrees. This means that the reference angle (difference between the two) is **45 degrees**.

Subtract 360° 360° from 460° 460° . The resulting angle of **100° 100°** is positive, less than 360° 360° and equivalent to 460° 460°.

Since **40°** is in the first quadrant, the reference angle is 40°.

Trigonometry examples

Find an angle that is positive, less than 360° and equivalent to 455°. Subtract 360° 360° from 455° 455° . The resulting angle of **95° 95°** is positive, less than 360° 360° and equivalent to 455° 455°.

- Cot(90° – 405°) = Cot(-315°)
- -Cot(90° + 405°) = -Cot 495°
- – tan(180° – 405°) = -tan(-225°)

The value of sin 405° is **equal to the y coordinate (0.7071)**. ∴ sin 405° = 0.7071.

Subtract 360° 360° from 435° 435° . The resulting angle of **75° 75 °** is positive, less than 360° 360 ° , and equivalent to 435° 435 ° .

Subtract 360° 360° from 570° 570° . The resulting angle of **210° 210°** is positive, less than 360° 360° and equivalent to 570° 570°.

Find an angle that is positive, less than 360° and equal to 675°. Subtract 360° 360° from 675° 675° . The resulting angle of **315°** 315° is positive, less than 360° 360° and equivalent to 675° 675°.

Find an angle that is positive, less than 360° and equal to 640°. Subtract 360° 360° from 640° 640° . The resulting angle of **280°** 280° is positive, less than 360° 360° , and coterminal with 640° 640° .

The reference angle of 170 is 190 – 170. That’s **20°**.

Reference angle for 290°: **70°** Reference angle for 295°: 65° Reference angle for 300°: 60° (π / 3)

Since 330 is thirty less than 360, and since 360° = 0°, then the angle 330° is thirty degrees below (ie, just before) the positive x-axis in the fourth quadrant. So its reference angle is **30°**.

The reference angle of 240° is **60°**.

If you look at a graph, there is a 150° angle in quadrant II, so the reference angle is θ’ = 180° – 150° = **30°**.

If the end face is in the second quadrant (angle from 90° to 180°), our reference angle is **180° minus our given angle**. So if our given angle is 110°, then its reference angle is 180° – 110° = 70°.

- https://www.mathway.com/popular-problems/Trigonometry/341509
- https://socratic.org/questions/how-do-you-find-the-exact-value-of-tan-405-degrees
- https://www.mathway.com/popular-problems/Trigonometry/341484
- https://www.mathway.com/popular-problems/Trigonometry/341515
- https://www.mathway.com/popular-problems/Trigonometry/341485
- https://www.youtube.com/watch?v=E-xFXpVo14o
- https://www.youtube.com/watch?v=8nccW3rXE2s
- https://www.cuemath.com/trigonometry/tan-405-degrees/
- https://www.cuemath.com/trigonometry/sin-405-degrees/
- https://www.mathway.com/popular-problems/Trigonometry/341511
- https://www.mathway.com/popular-problems/Trigonometry/311916
- https://www.mathway.com/popular-problems/Trigonometry/341205
- https://www.mathway.com/popular-problems/Trigonometry/341203
- https://www.onlinemath4all.com/finding-the-measure-of-the-reference-angle.html
- https://www.omnicalculator.com/math/reference-angle
- https://www.purplemath.com/modules/radians3.htm
- https://study.com/academy/answer/what-is-the-reference-angle-for-240-degrees.html
- http://www.biology.arizona.edu/biomath/tutorials/trigonometric/Trig4T.html
- https://www.piday.org/calculators/reference-angle-calculator/

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