Question

what is the reference angle in radians for 876°

Answer 1

First we should find the terminal side of 876° by subtracting 360° (for a full rotation) as many times possible until we get some where between 0° and 360°. Doing this we get 156° (876-360-360)

Second, knowing the unit circle, this measure is closest of the reference angle of 150°, which in radians is 5pi/4

I am not exactly sure if that is what you were asking for... I apologize if any of this is pooly explained

Answer 2

Answer with explanation:

Reference Angle is the smallest Positive angle that terminal side makes with the  x axis.

→→If angle lies in first Quadrant,then that Angle is equal to reference Angle.

For, Example, Angle between Initial and terminal side =40°

Reference Angle =40°

→→If angle lies in Second Quadrant,then, [180°- that Angle] is equal to reference Angle.

For, Example, Angle between Initial and terminal side =140°

Reference Angle =180°-140°=40°

→→If angle lies in Third Quadrant,then, [That Angle -180°] is equal to reference Angle.

For, Example, Angle between Initial and terminal side =220°

Reference Angle =220°-180°=40°

→→If angle lies in Fourth Quadrant,then, [360° -that Angle ] is equal to reference Angle.

For, Example, Angle between Initial and terminal side =290°

Reference Angle =360° - 290°=70°

⇒⇒Given Angle = 876°

First we will check out in which Quadrant it lies.

→876°=2 ×360°+156°

As,360° is equal to a revolution.

Angle 876° ,is equal to 156°,which lies in Second Quadrant.

So, Reference Angle of 156° is

= 180 ° -156°

= 24°→Reference angle  for 876°

⇒⇒360° = 2 π Radian

$1 ^{\circ}=[\frac{2\pi}{360^{\circ}}]^{c}\\\\24^{\circ}=[\frac{2\pi\times 24}{360^{\circ}}]^{c}\\\\24^{\circ}=[\frac{2\pi }{15}]^{c}$