Unit Circle & Trig Values

Drag a point around the unit circle or type an angle to see sin, cos and tan, with exact values such as √3/2 for special angles. Trig tables, a degree and radian converter and inverse functions are on the same page.

How to use

1. Type an angle in "Angle θ", such as 150, 150° or 5π/6, or drag the point around the unit circle.
2. Each function shows its "Exact value" and "Decimal", with the quadrant, signs, "Reference angle" and "Point (cos θ, sin θ)". The sine and cosine graphs move along.
3. Switch on "Snap to 15° steps" to stay on special angles. Exact values are shown only for multiples of 15°.
4. Use the tabs below for "Special angles", "Table 0–90°", "Printable circle", "Degrees ↔ radians" and "Inverse functions".

How it works

• The unit circle has a radius of 1. The point where the terminal side of angle θ meets the circle is (cos θ, sin θ), and tan θ = sin θ ÷ cos θ.
• "Table 0–90°" lists values in 1° steps, rounded to four decimal places. tan 90° is undefined.
• "Inverse functions" gives principal values from −90° to 90° for sin⁻¹, 0° to 180° for cos⁻¹ and between −90° and 90° for tan⁻¹.

Questions and answers

What are sin 30°, cos 30° and tan 30°?

sin 30° = 1/2, cos 30° = √3/2 and tan 30° = √3/3. At 45°, sin and cos are both √2/2 and tan 45° = 1.

How do I convert degrees to radians?

Multiply by π ÷ 180: 180° is π, 90° is π/2 and 60° is π/3 radians. For radians to degrees, multiply by 180 ÷ π.

What are the signs of sin, cos and tan in each quadrant?

In quadrant I all three are positive, in quadrant II only sin is positive, in quadrant III only tan is positive and in quadrant IV only cos is positive.

What is a reference angle?

It is the acute angle between the terminal side and the x-axis. The reference angle of 150° is 30°, and sin 150° equals sin 30°, which is 1/2.