Give an example of an angle theta in the domain 0 2 pi such

Give an example of an angle theta in the domain [0, 2 pi] such that cos(theta)

Solution

cos negative and tan negative

This means, sin = cos*tan = positive

Now, we know from sohcahtoa that.....

o/h = pos , a/h =negative and o/a = negative

Now, we know hypotenuse, h is ALWAYS POSITIVE

So, since sin = o/h = positive, opposite, o is also positive

Therefore, adjacent, a = negative

Now, where is opposite(y) positive and adjacent(x) negative?

x is negative and y is positibve in quadrant 2

So, we need to choose an angle within pi/2 to pi

And we can choose any of these standard angles :

2pi/3 , 3pi/4 , 5pi/6

Any of those will work