Cos theta = -4/9 with theta in quadrant 2, find sin theta

Question

I don’t know the answer .

Answer 1

There are 2 ways to answer this question.

 

First draw a figure to convince your self that the side opposite to the angle is 65^.5 an then that the sin is (65^.5)/9.

 

The other way is to look up the arc cos (-4/9) to find theta = 2.03135 then look up sin(2.03135).

 

Your answers should match.  Also remember the mnemonic "all sin tan cos" which it the trig function which is positive respectively in quadrants 1, 2, 3, 4.

Answer 2

In quadrant II, 

 

sinθ > 0 ⇒

 

sinθ = +√(1 - cos²θ) = +√[1 - (-4/9)]² = ?