Reference Angles

 

Reference help us remember certain trig values. As can been seen from the unit circle, the points on the circle are the same all around except for the negative signs. Basically, knowing the first quadrant values will you to know all of the angles.

 

Quadratal Angles

 

These are angles whose terminal sides are on the axis, multiples of 90^\circ or \frac{\pi}{2}. These angles separate the quadrants. They do not exist in any quadrant– only between.

 

Reference Angles

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The (x,y) and (\sin\theta,\cos\theta) are the same on each of these.

 

\sin\frac{\pi}{6}=\frac{1}{2}              \sin\frac{5\pi}{6}=\frac{1}{2}              \sin\frac{7\pi}{6}=-\frac{1}{2}              \sin\frac{11\pi}{6}=-\frac{1}{2}

 

\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}          \cos\frac{5\pi}{6}=-\frac{\sqrt{3}}{2}          \cos\frac{7\pi}{6}=-\frac{\sqrt{3}}{2}          \cos\frac{11\pi}{6}=\frac{\sqrt{3}}{2}

 

\tan\frac{\pi}{6}=\frac{1}{\sqrt{3}}          \tan\frac{5\pi}{6}=-\frac{1}{\sqrt{3}}          \tan\frac{7\pi}{6}=\frac{1}{\sqrt{3}}          \tan\frac{11\pi}{6}=-\frac{1}{\sqrt{3}}