cos a= 24/25 with 270˚

Question

cos a= 24/25 with 270˚<a<360˚ how do you find sin a?

nikolas · Answer

You know that the cosine ratio is x/r, and the sine ratio is y/r. You've been given x and r so you can use the Pythagorean theorem to solve for y. Then you should know the sine ratio, and you've also been told that sin a is in the fourth quadrant, so it will be a negative number.

nikolas · Answer

^That is, y will be negative and sin a will be y/r. Hope this makes sense.

anonymous · Answer

http://bamboodock.wacom.com/doodler/91950f0c-1c9b-45a6-9264-0bfc5092e7b9

anonymous · Answer

could you help me

nikolas · Answer

Sorry I'm not too sure about that one... are you saying that somehow$$\sin a = -\sqrt{1-\cos ^{2}a}?$$

anonymous · Answer

yes in the book it said to find sin a

anonymous · Answer

i dont know why it's a negative

nikolas · Answer

Does the question give any more information? We know that usually the square root would be positive, so I'm assuming that because it's negative, this means that the value of sin(a) must be negative? That would mean the angle is in the third or fourth quadrant, between 180 degrees and 360 degrees.

I'm not entirely sure but I think that's it.

anonymous · Answer

well since 270˚<a<360˚ its on the 4th quadrant does that mean its negative?

nikolas · Answer

Yes, the sine ratio of an angle will be negative in the 4th quadrant, because the value of "y" will be negative. More info here: http://www.mathsisfun.com/algebra/trig-four-quadrants.html