Create an algebraic sinusoidal model relating the rotation angle to blade height above the table.

Question

Rotation Angle ()	Related Acute Angle ()	Exact value of sin()	Height of Blade above Table (cm)
0°	90	0	15
30°	60	0.5	20
45°	45	0.71	22
60°	30	0.87	24
90°	0	1	25
120°	60	0.87	24
135°	45	0.71	22
150°	30	0.5	20
180°	0	0	15
210°	60	-0.5	10
225°	45	-0.71	8
240°	30	-0.87	6
270°	0	-1	5
300°	60	-0.87	6
315°	45	-0.71	8
330°	30	-0.5	10
360°	0	0	15

Answer 1

Note: The 1st point on your plot should be (0,15) instead of (15,0).

The max and min height values are 25 and 5, so the midline of the sine function is at y = 15 cm and the amplitude is 10 cm. The max occurs at 90° and the min at 270°, so there is no phase shift. Therefore Blade Height = 10 sin θ + 15.

If the blade length of 10 cm is decreased by 3 cm, then the characteristics of the curve remain the same except for the range and amplitude, and BH = 7 sin θ + 15.