Syntax. SIN(number)

Definition. This function returns the sine of a number.

Argument

Background. In a right triangle, the ratio between the hypotenuse and the opposite leg depends on the apex angle. The ratio between the opposite leg of an angle and the hypotenuse is the sine (sin) of an angle.

The SIN() function requires radians for calculations. If the angle is specified in degrees, you have to multiply the angle by PI()/180 or convert it with the RADIANS() function.

The sine of angle α in an unit circle (c = 1) increases up to 90° and has the value 1 in this angle (see Figure 16-27).

Figure 16-27. Sine in a unit circle.

In a coordinate system, the angle α on the x-axis and the sine of α on the y-axis result in the curve shown in Figure 16-28.

Figure 16-28. Sine curve.

Example. Suppose you want to calculate the height of a mountain. The distance between the observation station and the mountaintop is 3.7 miles. The mountaintop appears at an angle of 19.5°. The formula for the sine is:

You enter the existing information in the formula

Here is the equation to calculate the height:

Height = sin(19.5) • 3.7

The result is:

Height = 1.235 miles ≈ 6,521 feet

Enter the following formula in the formula bar:

=SIN(RADIANS(19.5)) • 3.7

For Excel to be able to calculate the sine for the angle of 19.5°, the angle has to be converted to radians. Then the sine is multiplied by the hypotenuse.

To return the result in feet, you must round the result to three digits and multiply by 5,280.

=ROUND((SIN(RADIANS(19.5)) • 3.7),3) • 5280