# Why do reference angles work?

Space and AstronomyReference angles **make it possible to evaluate trigonometric functions for angles outside the first quadrant**. They can also be used to find (x,y) coordinates for those angles. We will use the reference angle of the angle of rotation combined with the quadrant in which the terminal side of the angle lies.

## What is true about the reference angle?

The reference angle is **always positive**. In other words, the reference angle is an angle being sandwiched by the terminal side and the x-axis. It must be less than 90 degree, and always positive.

## Why the reference angle is same?

It is the angle between the terminal side and the x axis. As the point moves into each quadrant, note how **the reference angle is always the smallest angle between the terminal side and the x axis**.

Finding the reference angle.

Quadrant | Reference angle for θ |
---|---|

1 | Same as θ |

2 | 180 – θ |

3 | θ – 180 |

4 | 360 – θ |

## Why is it important to identify the reference angle in a right triangle?

Reference triangles are used **to find trigonometric values for their standard position angles**. They are of particular importance for standard position angles whose terminal sides reside in quadrants II, III and IV.

## What does the reference angle determine?

So, if our given angle is 110°, then its reference angle is 180° – 110° = 70°. **When the terminal side is in the third quadrant (angles from 180° to 270°), our reference angle is our given angle minus 180°**. So, if our given angle is 214°, then its reference angle is 214° – 180° = 34°.

## What do you need to keep in mind when trying to find the reference angle?

Video quote: *You minus the angle in quadrant two if the angle is in Quadrant three the reference angle is going to be the angle in quadrant three minus 180.*

## Can a reference angle be negative?

**The reference angle of an angle is always non-negative** i.e., a negative reference angle doesn’t exist. The reference angle of any angle always lies between 0 and π/2 (both inclusive).

## Is a reference angle always acute?

A reference angle for a given angle in standard position is the positive acute angle formed by the $x$-axis and the terminal side of the given angle. Reference angles, by definition, **always have a measure between 0 and .**

## Can reference angles be zero?

**A reference angle can be zero**: this happens when the original angle’s terminal point lies on the x -axis. That is, the reference angle is zero whenever the original angle’s terminal point is either (1,0) or (−1,0) .

## What is the reference angle of 225 degrees?

45°

Reference angle for 225°: **45°** (π / 4)

## What is the reference angle of 810?

90°

Since **90°** is in the first quadrant, the reference angle is 90° .

## What is the exact value of tan150?

-0.5774

FAQs on Tan 150 Degrees

Tan 150 degrees is the value of tangent trigonometric function for an angle equal to 150 degrees. The value of tan 150° is -1/√3 or **-0.5774** (approx).

## What is the reference angle for 330?

30 degrees

Since the absolute value of negative 330 degrees is simply 330 degrees, we have this angle plus 𝛼 equals 360 degrees. We can then subtract 330 degrees from both sides, giving us 𝛼 is equal to **30 degrees**. This is the reference angle for negative 330 degrees.

## How do you draw a 210 degree angle?

Video quote: *But we have to draw 210 degree so we have to add with 180 degree by 30 degree angle. So if you add 30 degree angle with 180 degree then we can get 210 degree angle okay.*

## What is the reference angle for 135?

45′

135′ is in the second quadrant, so our reference angle is 180′-135 “, or **45′** .

## What is the reference angle for 120 degrees?

Since the angle 120° is in the second quadrant, **subtract 120° from 180°** .

## What is the reference angle for 210?

The reference angle is found by calculating the difference between θ and the x-axis. In this problem, 210 is closest to 180, so 210∘−180∘=**30∘** .

## What is the reference angle for 230 degrees?

Trigonometry Examples

Since the angle **180°** is in the third quadrant, subtract 180° from 230° .

## What is the reference angle of 300?

60 degrees

360 – 300 = **60 degrees**. The reference angle for 300 is 60 degrees.

## What is the reference angle for 720 degrees?

Subtract 360° 360 ° from 720° 720 ° . The resulting angle of **360° 360 °** is positive, less than 360° 360 ° , and coterminal with 720° 720 ° .

## What is the reference angle for 65 degrees?

65°

Trigonometry Examples

Since 65° is in the first quadrant, the reference angle is **65°** .

## What is the reference angle for an angle of 115?

Since the angle 115° is in the second quadrant, **subtract 115° from 180°** .

## What is the negative Coterminal of 115?

-245°

Coterminal Angles

115° Can you think of another angle whose terminal side will be the same as the 115° angle shown to the right? 115° 115 – 360 = **-245°** Try starting at the initial side and going clockwise (this is a negative angle).

## What is the reference angle for an angle that measures 91?

180°

Trigonometry Examples

Since the angle 91° is in the second quadrant, **subtract 91° from 180°** .

## What is the reference angle for a 240 angle?

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

## What is the reference angle if the angle is measured at 63?

63°

Trigonometry Examples

Since 63° is in the first quadrant, the reference angle is **63°** .

## How do you use reference angles to evaluate trigonometric functions?

Video quote: *The reference angle is the angle between the terminal side and the x-axis. So you can see that it has to be the difference between 360. And 300. So the reference angle is 60.*

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