Sines, cosines and tangeantes of common angles

Introduction

This page lists the values sines, cosines and tangeantes of common (noteworthy) angles. The following illustration shows the common angles on the unit circle (only for cosines and sines):

Sines and cosines of common angles on the unit circle

Table of sines, cosines and tangeantes

The following table shows the sines and cosines of common angles in radians and in degrees

Radians Degrees Cosine Sinus Tangent
0 0 1 0 0
\( \frac{ \pi }{6} \) 30 \( \frac{\sqrt{3}}{2} \) \( \frac{1}{2} \) \( \frac{ \sqrt{3}}{3} \)
\( \frac{ \pi }{4} \) 45 \( \frac{\sqrt{2}}{2} \) \( \frac{\sqrt{2}}{2} \) 1
\( \frac{ \pi }{3} \) 60 \( \frac{1}{2} \) \( \frac{\sqrt{3}}{2} \) \( \sqrt{3} \)
\( \frac{ \pi }{2} \) 90 0 1 -
\( \frac{ 2\pi }{3} \) 120 \( -\frac{1}{2} \) \( \frac{\sqrt{3}}{2} \) \( -\sqrt{3} \)
\( \frac{ 3\pi }{4} \) 135 \( -\frac{\sqrt{2}}{2} \) \( \frac{\sqrt{2}}{2} \) -1
\( \frac{ 5\pi }{6} \) 150 \( -\frac{\sqrt{3}}{2} \) \( \frac{1}{2} \) \( -\frac{ \sqrt{3}}{3} \)
\( \pi \) 180 -1 0 0
\( \frac{ 7\pi }{6} \) 210 \( -\frac{\sqrt{3}}{2} \) \( -\frac{1}{2} \) \( \frac{ \sqrt{3}}{3} \)
\( \frac{ 5\pi }{4} \) 225 \( -\frac{\sqrt{2}}{2} \) \( -\frac{\sqrt{2}}{2} \) 1
\( \frac{ 4\pi }{3} \) 240 \( -\frac{1}{2} \) \( -\frac{\sqrt{3}}{2} \) \( \sqrt{3} \)
\( \frac{ 3\pi }{2} \) 270 0 -1 -
\( \frac{ 5\pi }{3} \) 300 \( \frac{1}{2} \) \( -\frac{\sqrt{3}}{2} \) \( -\sqrt{3} \)
\( \frac{ 7\pi }{4} \) 315 \( \frac{\sqrt{2}}{2} \) \( -\frac{\sqrt{2}}{2} \) -1
\( \frac{ 11\pi }{6} \) 330 \( \frac{\sqrt{3}}{2} \) \( -\frac{1}{2} \) \( -\frac{ \sqrt{3}}{3} \)
\( 2\pi \) 360 1 0 0

See also


Last update : 06/11/2018