Grade 12 trig problem solving?

Question

A crank 20 cm long, starting at 60 degrees from the horizontal, sweeps out a positive angle at the uniform rate of 10 rad/s.

Determine a function that gives the height of the end of the crank from the horizontal line at any time t.

Someone please help me on this question, but trying to figure it out for a while now.

Answer 1

In radians, the crank starts off at an angle of π/3 and the angle increases by 10 every second. So the angle as a function of time (t) is π/3 + 10t.

The height of the crank in cm is the length of the crank multiplied by the sine of the angle it makes with the horizontal (basic trig), so the height in cm at time t seconds is given by

h(t) = 20 sin (π/3 + 10t)

Answer 2

Draw a circle. Now, draw a horizontal line (180 degrees). Now draw a line making a 60 degree angle. At the end of this line is the handle of the crank.
We get:
angle = (pi)/3 + 10t .... for t seconds in radians
hypotenuse = 20
one leg = x
sin( (pi)/3 + 10s ) = x/20
20*sin( (pi)/3 + 10t ) = x
labeled as cm in t seconds

Answer 3

edasay