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?

1 Answer
Dec 5, 2017

Here is the sketch:
enter image source here

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#