What is a reference angle unit circle?

For each angle drawn in standard position, there is a related angle known as a reference angle. This is the angle formed by the terminal side and the x-axis. The reference angle is always considered to be positive, and has a value anywhere from 0° to 90°. Two angles are shown below in standard position.

How do you find the reference angle on a unit circle?

Video quote: And we're going to subtract 180 from it to find the reference angle. So this one's just going to be 60 degrees. So it's the given angle minus 180.

What is reference angle?

When an angle is drawn on the coordinate plane with a vertex at the origin, the reference angle is the angle between the terminal side of the angle and the x-axis. The reference angle is always between 0 and 2π radians (or between 0 and 90 degrees).

How do you find the reference angle?

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 is reference angle on the unit?

What is a reference angle. Reference Angle: the acute angle between the terminal arm/terminal side and the x-axis. 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.

How many reference angles are there in the unit circle?

Look at the degrees unit circle, and you will see that the reference angles are 0, 30, 45, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, and 330 degrees. The equivalent angles in radians are 0, pi/6, pi/4, pi/3, pi/2, 2pi/3, 3pi/4, 5pi/6, pi, 7pi/6, 5pi/4, 4pi/3, 3pi/2, 5pi/3, 7pi/4, and 11pi/6.

What is reference angle and examples?

For example, to find the reference angle of -1000°, we will add 360° three times to it. It implies, – 1000° + 3(360°) = -1000° + 1080° = 80°. Therefore, 80° is the required reference angle of a negative angle of -1000°. If θ in a negative angle -θ is from 0 to 90 degrees, then its reference angle is θ.

What is the reference angle of 235?

55 degrees

The reference angle for 235 is 55 degrees. If the terminal side of the angle is in the fourth quadrant, we take the angle and subtract it from 360 degrees.

What is the reference angle of 120?

60°

Reference angle for 120°: 60° (π / 3)

What is the reference angle of 210?

210 degrees is 30 degrees past 180, which means the reference angle is 30 degrees.

What is the reference angle of 320?

40°

Trigonometry Examples



Add 360° 360 ° to −320° – 320 ° . The resulting angle of 40° 40 ° is positive and coterminal with −320° – 320 ° . Since 40° is in the first quadrant, the reference angle is 40° .

What is the reference angle for 290?

Since the angle 290° is in the fourth quadrant, subtract 290° from 360° .

What is the reference angle of 315?

45∘

So, the reference angle is 360∘−315∘=45∘ . ∴ We have found the reference angle for 315 degrees as 45∘ .

What is the reference angle of 330?

30°

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

What is the reference angle of 150?

30°

Looking at a graph, a 150° angle lies in quadrant II, therefore the reference angle is θ’ = 180° – 150° = 30°.

What is the reference angle of 215?

Add 360° 360 ° to −215° – 215 ° . The resulting angle of 145° 145 ° is positive and coterminal with −215° – 215 ° .

What is the reference angle of 345?

The reference angle of 345 is 360 – 345. That is 15°.

What is the reference angle of 225 degrees?

Trigonometry Examples



Since the angle 180° is in the third quadrant, subtract 180° from 225° .

What is the Coterminal angle of 216?

Trigonometry Examples



The resulting angle of 144° 144 ° is positive and coterminal with −216° – 216 ° . Since the angle 144° is in the second quadrant, subtract 144° from 180° .

What is the reference angle for 275?

Since the angle 275° is in the fourth quadrant, subtract 275° from 360° .

What is the reference angle of 410?

Subtract 360° 360 ° from 410° 410 ° . The resulting angle of 50° 50 ° is positive, less than 360° 360 ° , and coterminal with 410° 410 ° .

What is the reference angle of 1230?

Trigonometry Examples



Subtract 360° 360 ° from 1230° 1230 ° . The resulting angle of 870° 870 ° is positive and coterminal with 1230° 1230 ° but isn’t less than 360° 360 ° .

What is the reference angle of 540?

Subtract 360° 360 ° from 540° 540 ° . The resulting angle of 180° 180 ° is positive, less than 360° 360 ° , and coterminal with 540° 540 ° .

What is the reference angle for 400?

40°

Trigonometry Examples



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

What is the reference angle of 80?

80°

Trigonometry Examples



Since 80° is in the first quadrant, the reference angle is 80° .

What is the reference angle of 45?

Trigonometry Examples



Since 45° is in the first quadrant, the reference angle is 45° .

What is the reference angle of 85?

Trigonometry Examples



Since 85° is in the first quadrant, the reference angle is 85° .