§15.7. Trigonometry

We have twelve functions left to cover, though they are all closely related.

(real number)** degrees ... real number**

Inform measures angles in radians, a convention in which the angle for a half circle is pi, and a right angle is pi divided by 2. This is better from a mathematical point of view, but in practice most people think about angles using degrees, where 180 degrees is a half-circle and a right angle is 90 degrees. This phrase helps with that by converting from degrees to radians: in other words, it multiplies by 0.0174532925, since that's roughly 1/180th of pi. Examples:

sine of 90 degrees = 0.0

cosine of 60 degrees = 0.5

**sine of **(real number)** ... real number**

The length of the upright of a right-angled triangle with this angle and a hypotenuse of length 1, where angle is measured in radians. Examples:

sine of 0 = 0

sine of 45 degrees = 0.70711

sine of (pi divided by 4) = 0.70711

sine of (pi divided by 2) = 1.0

sine of pi = 0

**cosine of **(real number)** ... real number**

The length of the base of a right-angled triangle with this angle and a hypotenuse of length 1, where angle is measured in radians. Examples:

cosine of 0 = 1.0

cosine of 45 degrees = 0.70711

cosine of (pi divided by 4) = 0.70711

cosine of (pi divided by 2) = 0.0

cosine of pi = -1.0

**tangent of **(real number)** ... real number**

The ratio of the upright length to the base length in a right-angled triangle with this angle and a hypotenuse of length 1, where angle is measured in radians. Examples:

tangent of 0 = 0.0

tangent of 45 degrees = 1.0

tangent of (pi divided by 4) = 1.0

tangent of (pi divided by 2) = plus infinity

**hyperbolic sine of **(real number)** ... real number**

The hyperbolic sine function, often written "sinh" but pronounced "shine".

**hyperbolic cosine of **(real number)** ... real number**

The hyperbolic cosine function, often written "cosh".

**hyperbolic tangent of **(real number)** ... real number**

The hyperbolic tangent function, often written "tanh".

**hyperbolic arccosine of **(real number)** ... real number**

The inverse of the hyperbolic cosine function.

**hyperbolic arctangent of **(real number)** ... real number**

The inverse of the hyperbolic tangent function.