Trigonometry Graphs

The trigonometric functions are periodic. The table of standard angles and the unit circle below are lookup keys for the most common exact values. Sine and cosine are bounded sinusoids of period 2π. Tangent and cotangent have period π with vertical asymptotes. Secant and cosecant inherit asymptotes from the zeros of cosine and sine.

Exact values at first-quadrant angles, from 30-60-90 and 45-45-90 right triangles.

Angle	0	30	45	60	90
$\sin\theta$	0	$\frac{1}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{3}}{2}$	1
$\cos\theta$	1	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{1}{2}$	0
$\tan\theta$	0	$\frac{\sqrt{3}}{3}$	1	$\sqrt{3}$	$\theta$

Sine: bounded in [-1, 1], period 2π, odd.

Cosine: sine shifted by π/2, same amplitude and period, even.

Tangent: period π, asymptotes at odd multiples of π/2.

Cotangent: reciprocal of tangent, asymptotes at zeros of sine.

Secant: reciprocal of cosine, unbounded near cosine’s zeros.

Cosecant: reciprocal of sine, unbounded near sine’s zeros.

Unit Circle

The unit circle maps each angle to a point (cos θ, sin θ) on the circle of radius one. Every standard trig value is a coordinate.