Question

Identify the reference angle es001-1. Jpg for each given angle, es001-2. Jpg. Es001-3. Jpg degrees. Es002-1. Jpg degrees. Es003-1. Jpg degrees. Es004-1. Jpg degrees.

Answer 1

The reference angle is the smallest angle between the terminal side and the x-axis.

$(1)\ \theta = 300^o$

300 degrees is in the 4th quadrant.

So, the reference angle is

$\alpha = 360 - \theta$

$\alpha = 360 - 300$

$\alpha = 60^o$

Hence, the reference angle of 300 degrees is 60 degrees

$(2)\ \theta = 225^o$

225 degrees is in the 3rd quadrant.

So, the reference angle is

$\alpha = \theta - 180$

$\alpha = 225 - 180$

$\alpha = 45^o$

Hence, the reference angle of 225 degrees is 45 degrees

$(3)\ \theta = 480^o$

480 degrees is in the 2nd quadrant (i.e. 480 - 360 = 120)

So, the reference angle is

$\alpha = 180 - \theta$

$\alpha = 180 - 120$

$\alpha = 60^o$

Hence, the reference angle of 480 degrees is 60 degrees

$(2)\ \theta = -210^o$

-210 degrees is in the 2nd quadrant (i.e. 360 - 210 = 150)

So, the reference angle is

$\alpha = 180 - \theta$

$\alpha = 180 - 150$

$\alpha = 30^o$

Hence, the reference angle of -210 degrees is 30 degrees

Read more about reference angles at:

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Answer 2

Answer:

⇒ 60 degrees

⇒ 45 degrees.

 ⇒ 60 degrees.

⇒ 30 degrees.

Explanation: