The three ratios
Sine, cosine and tangent compare the sides of a right-angled triangle. For an angle, sine is the opposite side over the hypotenuse, cosine is the adjacent over the hypotenuse, and tangent is the opposite over the adjacent.
For 30 degrees, sine is 0.5, cosine is 0.866025 and tangent is 0.57735.
Working back from a ratio
Choose the angle mode and pick which ratio you have. A sine of 0.5 gives 30 degrees, or 0.523599 radians.
Sine and cosine can only be between -1 and 1, because they compare a side with the hypotenuse, which is never shorter. Tangent has no such limit.
Degrees and radians
One full turn is 360 degrees or 2 pi radians, so one radian is about 57.2958 degrees.
The angle unit you pick applies to the angle you type. Every answer is given in both degrees and radians, so you never have to convert by hand.
Where tangent runs out
Tangent is undefined at 90 and 270 degrees, where the cosine is zero, because the ratio would divide by zero.
At those angles the tangent row is left out instead of showing a huge number that looks like a real answer.
Inputs for the trig calculator
What do you want to work out?
Choose the ratios for an angle, or the angle for a ratio.
Angle
The angle to take the ratios of, in the unit you choose below. It can be negative or more than a full turn.
Ratio value
The sine, cosine or tangent you already know. A sine or cosine must be between -1 and 1.
Which ratio is it?
Tells the calculator which inverse to use when working back to an angle.
Angle unit
Degrees or radians for the angle you type. Answers are shown in both.
CALCULATOR QUESTIONS
Trig calculator questions
What is sin 30?
0.5. Cos 30 is 0.866025 and tan 30 is 0.57735.
How do I find an angle from a sine?
Choose the angle mode, pick sine and enter the value. A sine of 0.5 gives 30 degrees.
Why can sine not be more than 1?
Sine is the opposite side divided by the hypotenuse, and the hypotenuse is always the longest side, so the ratio cannot exceed 1.
What is the difference between degrees and radians?
Both measure the same angle. A full turn is 360 degrees or 2 pi radians, so 180 degrees is pi radians.