.
Changes in sin 8 and cos 8
As we work with sine and cosine functions with components, it's useful to know how the two change as
e increases or decreases:
.
.
Since the horizontal component of a vector depends on cos 8, it will follow the change in cosas
increases or decreases. The vertical component will do the same for sin 8. Thus we can recognize that:
and the y-component equal zero, cos 0 and the x-component are a maximum
At 8 = 90°, sin 8 and the y-component are a maximum, cos 8 and the x-component equal zero
At = 0º, sin
y = sin x
As 8 increases, sin 8 increases and cos 8 decreases
As 9 decreases, sin 8 decreases and cos 0 increases
4. A sled of mass M is pulled to the right with a tension force of T at an angle of 0°. There is negligible
friction on the sled.
a. Draw a free-body diagram for the sled
b. Derive an expression for the normal force on the sled.
y = cos x
c. Derive an expression for the acceleration of the sled.
Horizontal surface
d. How would the magnitude of the normal force change if the angle of the tension force
increased? Briefly justify your answer.