Unit Circle Problems solve cosW=sin20, sinW=cos(-10), sinW< 0.5 and 1<tanW

Naidely

New member
Without a calculator, find all solutions w between 0 and 360, inclusive, providing diagrams that support your results.

1) cosW=sin20

2) sinW=cos(-10)

3) sinW< 0.5

4) 1<tanW

Country Boy

Well-known member
MHB Math Helper
You titled this "unit circle problems". Have you drawn a unit circle? Do you know that, at each (x, y) point on the circle, $$x= cos(\theta)$$ and $$y= sin(\theta)$$? Where is sin(20) on that circle? So for what angle is cos(W)= sin(20)?

Naidely

New member
yes im aware that y= sin(theta) and x= cos(theta)
and yes I drew my unit circle
so sin20 is in the first quadrant but im not sure how to import images here, if possible
and cos70= sin 20, I figured that out a few days ago, however im stuck on 3 and 4

Country Boy

Well-known member
MHB Math Helper
Instead of using a unit circle, for 3 and 4, draw the graphs of y= sin(x) and y= tan(x). Compare the graph of y= sin(x) with the graph of y= 1/2 and compare the graph of y= tan(x) with y= 1. You should know that sin(x)= 1/2 for $$\pi/6$$ radians (30 degrees) and $$5\pi/6$$ radians (150 degrees) and that tan(x)= 1 for $$\pi/4$$ radians (45 degrees) and $$5\pi/4$$ radians (225 degrees). (There is a nice graphing app at https://www.desmos.com/calculator.)