TrigLab

Trigonometry Calculator

Enter degrees — get all three ratios.

Angle (degrees)

Or drag the point around the circle below

sin(θ): 0.5
cos(θ): 0.866
tan(θ): 0.577

What you entered

Angle: 30°

1
Convert degrees to radians
30 × π ÷ 180= 0.5236
2
sin(θ)
sin(30°)= 0.5
3
cos(θ)
cos(30°)= 0.866
4
tan(θ) = sin(θ) ÷ cos(θ)
tan(30°)= 0.5774

Result

sin(θ): 0.5

At 30°, sin = 0.5, cos = 0.866, tan = 0.577.

Sine, cosine and tangent at common angles

Values for the standard angles, rounded to four decimals. Tangent is sine divided by cosine, so it is undefined wherever cosine is zero.

Angle	sin	cos	tan
0 deg	0.0000	1.0000	0.0000
30 deg	0.5000	0.8660	0.5774
45 deg	0.7071	0.7071	1.0000
60 deg	0.8660	0.5000	1.7321
90 deg	1.0000	0.0000	undefined
120 deg	0.8660	-0.5000	-1.7321
180 deg	0.0000	-1.0000	0.0000
270 deg	-1.0000	0.0000	undefined

At 45 degrees sine and cosine are equal at 0.7071, which is 1 over the square root of 2, and that is why tangent is exactly 1 there. Tangent is undefined at 90 and 270 degrees because cosine is zero and the division has no value - the function shoots to infinity either side. Sine and cosine are the same curve shifted by 90 degrees, which the 30 and 60 degree rows show: sin 30 equals cos 60. Both are bounded between -1 and 1, so any calculation returning a sine above 1 has an error upstream.

Ratios on the unit circle

sin and cos describe the vertical and horizontal position of a point moving around a circle of radius 1 as the angle changes; tan is simply their ratio (sin ÷ cos), describing slope or steepness.

Where trig is used constantly

Construction (roof pitch, stair angles), navigation (bearing and distance), and any physics problem involving angled forces or motion all lean on these three ratios.

Frequently asked questions

A 20-foot ladder leans against a wall at 70° — how high up the wall does it reach?

The height is the side opposite the 70° angle: height = 20 × sin(70°) = 20 × 0.9397 ≈ 18.79 feet. The base distance from the wall is 20 × cos(70°) ≈ 6.84 feet.

What's the difference between sin, cos, and tan?

In a right triangle: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent (which also equals sin/cos). The mnemonic SOH-CAH-TOA captures all three. Each ratio isolates a different relationship between the angle and two sides.

My calculator gives sin(90°) = 0.8939 — what's wrong?

Your calculator is probably set to radians instead of degrees. In radians, 90 is a huge angle (over 14 full rotations). Switch to degree mode, or convert: 90° = π/2 radians ≈ 1.5708 radians. The angle converter can help with conversions.

When do I use inverse trig functions (arcsin, arccos, arctan)?

When you know the ratio and need the angle. If a ramp rises 3 feet over a 12-foot run, the angle is arctan(3/12) = arctan(0.25) ≈ 14.04°. Regular trig goes angle → ratio; inverse trig goes ratio → angle.

Why does tan(90°) give an error or 'undefined'?

At 90°, cos(90°) = 0, and tan = sin/cos. Dividing by zero is undefined. Geometrically, a 90° angle in a right triangle would make the 'adjacent' side zero length — the triangle degenerates into a vertical line with infinite slope.