Question

If you sketch a unit circle with angle θ in standard position: For what values of θ is the sine increasing? Decreasing?

For what values of θ is the cosine increasing? Decreasing?
For which angle between 0° and 360° is sine equal to 0? Where is cosine equal to 0?

Answer 1

Here is the sketch:

Explanation:

The above diagram was drawn in radians, to convert to degrees:
`color(white)("XXX")pi/2 = 90^circ`
`color(white)("XXX")pi=180^circ`
`color(white)("XXX")(3pi)/2=270^circ`

For
#color(white)("XXX"){:(theta=,color(white)("xxx"),cos(theta)=), (0,,+1), (90^circ,,0), (180^circ,,-1), (270^circ,,0), (360^circ,,+1) :}#
and we can see that `cos(theta)`
`color(white)("XXX")`decreases from `theta=0` to `theta=180^circ`
and
`color(white)("XXX")`increases from `theta=180^circ` to `theta=360^circ`