Are Coterminal angles and reference angles the same?

Coterminal angles are equal angles. To find a coterminal of an angle, add or subtract \(360\) degrees (or \(2π\) for radians) to the given angle. Reference angle is the smallest angle that you can make from the terminal side of an angle with the \(x\)-axis.

Is the reference angle a Coterminal angle?

Video quote: This angle would also end up in the same spot as you can see I'm going to draw a line right over that one would be in the same place.

What is the difference of Coterminal and reference angle?

Coterminal angles are angles that share the same terminal side. A reference angle is the size of the smallest acute angle, t, formed by the terminal side of the angle t and the horizontal axis.

What is a 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).

What are Coterminal angles?

Coterminal angles: are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example, the angles 30°, –330° and 390° are all coterminal (see figure 2.1 below). Fig. 2.1.

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°.

How do reference angles work?

The reference angle is the angle that the given angle makes with the x-axis. Regardless of where the angle ends (that is, regardless of the location of the terminal side of the angle), the reference angle measures the closest distance of that terminal side to the x-axis.

How do I find my reference number?

Video quote: To find five pi divided by eight on our unit circle we'll first divide our circle into pi or eight eight sections in the upper semicircle. Just making rough drawing. Here.

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 570?

Subtract 360° 360 ° from 570° 570 ° . The resulting angle of 210° 210 ° is positive, less than 360° 360 ° , and coterminal with 570° 570 ° .

What is the reference angle of 520?

Find an angle that is positive, less than 360° , and coterminal with 520° . Subtract 360° 360 ° from 520° 520 ° . The resulting angle of 160° 160 ° is positive, less than 360° 360 ° , and coterminal with 520° 520 ° .

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 of 120?

60°

Reference angle for 120°: 60° (π / 3)

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 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 200?

20

A 200-degree angle is between 180 and 270 degrees, so the terminal side is in QIII. Do the operation indicated for that quadrant. Subtract 180 degrees from the angle, which is 200 degrees. You find that 200 – 180 = 20, so the reference angle is 20 degrees.

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 225 degrees?

Trigonometry Examples



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

What is the reference angle for 285?

Since the angle 285° is in the fourth quadrant, subtract 285° from 360° .

What is the reference angle in degrees for 31π 6?

The reference angle is 7π6 .

What is the reference angle of 7π 4?

π4

Since π4 is in the first quadrant, the reference angle is π4 .

What is the reference angle for 100 degrees?

80°

The terminal side is in Quadrant II. The original angle and the reference angle together form a straight line along the x-axis, so their sum is 180°. Therefore, the reference angle is 80°. The reference angle for 100° is 80°.

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 160?

Since the angle 160° is in the second quadrant, subtract 160° from 180° .