If you sketch a unit circle with angle θ in standard position...?

Question

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?

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Answer 1 · 2018-02-26T11:51:18

See below.

enter image source here

Looking at the graph of the sine function, we can see that.

In quadrant I the ratio is increasing from. #0->1#, #color(white)(88)bb(0<=theta<=90^@)#

In quadrant II the ratio is decreasing from. #1->0#, #color(white)(88)bb(90^@<=theta<=180^@)#

In quadrant III the ratio is decreasing from. #0->-1#, #color(white)(88)bb(180<=theta<=270^@)#

In quadrant IV the ratio is increasing from. #-1->0#, #color(white)(88)bb(270<=theta<=360^@)#

For the cosine function we have:

enter image source here

In quadrant I the ratio is decreasing from. #1->0#, #color(white)(88)bb(0<=theta<=90^@)#

In quadrant II the ratio is decreasing from. #0->-1#, #color(white)(88)bb(90^@<=theta<=180^@)#

In quadrant III the ratio is increasing from. #-1->0#, #color(white)(88)bb(180<=theta<=270^@)#

In quadrant IV the ratio is increasing from. #0->1#, #color(white)(88)bb(270<=theta<=360^@)#

We can see from the sine graph that #sin(theta)=0# at

#0^@,180^@,360^@#

And from the cosine graph #cos(theta)=0#

At:

#90^@,270^@#