SIN

Returns the sine of the given angle (in radians).

SIN(angle)

returns the (trigonometric) sine of angle, the angle in radians.To return the sine of an angle in degrees, use the RADIANS function.

SIN(PI()/2)

returns 1, the sine of PI/2 radians

SIN(RADIANS(30))

returns 0.5, the sine of 30 degrees

A Ferris Wheel

Let's imagine a Ferris wheel with the following characteristics:

We can model the height of a passenger pod on this Ferris wheel using a sine function. The general form of the sine function for this scenario is:

H(t)=Asin(B(t−C))+D

Where:

H(t) is the height of the pod in meters at time t in minutes.
A is the amplitude, which is the radius of the wheel, so A=50.
D is the vertical shift, which is the height of the center of the wheel, so D=55.
The period is 20 minutes. The value of B is calculated as B=2π/period=2π/20=π/10.
C is the horizontal shift. Let's assume we start our timer (t=0) when the pod is at its lowest point. The standard sine function starts at the midline, but a negative sine function starts at the lowest point. So we will use a negative sine function, which effectively shifts the standard sine function. The equation becomes: H(t)=−Asin(Bt)+D.

Putting it all together, the equation for the height of the pod is:

H(t)=−50sin(10πt)+55

Let's use this function to calculate the height of the pod at various times during its rotation.

	Time (minutes)	Calculation	Height (meters)	Description
	A	B	C	D
1	0	H(0) = -50sin(0) + 55	55	The pod starts at the midline (at the same height as the center).
2	5	H(5) = −50sin(π/10*5)+55=−50sin(π/2)+55=−50(1)+55	5	The pod is at its lowest point (55 - 50).
3	10	H(10)=−50sin(π/10*10)+55=−50sin(π)+55=−50(0)+55	55	The pod is back at the midline.
4	15	H(15)=−50sin(π/10*15)+55=−50sin(3π/2)+55=−50(−1)+55	105	The pod is at its highest point (55 + 50).
5	20	H(20)=−50sin(π/10*20)+55=−50sin(2π)+55=−50(0)+55	55	The pod completes one full rotation and is back at the midline.