Find the exact value of the expression:
cos [tan^-1 (-4/7)]

Question

Find the exact value of the expression:
cos [tan^-1 (-4/7)]

noelgreco · Answer

Remember, the trig function of an angle is a number, the inverse trig function of a number is an angle.

The best way to evaluate these problems is to draw a picture:
|dw:1364172334218:dw|

Now, what's the cosine of that angle?

anonymous · Answer

I'm not sure, I haven't seen it put this way o;

noelgreco · Answer

Well, if you don't do it like this you will continue to struggle.

I'm going to dinner.  Try to understand.

anonymous · Answer

Uh, we've been using the unit circle and such

noelgreco · Answer

The UNIT circle is used to get you to understand and derive the values of the 6 trig functions.  You should have that under your belt by now.

At this point you're going to allow the length of the terminal side of the angle to be any number, not just the 1 of the unit circle.

I'll draw it in greater detail:
|dw:1364175044362:dw|
Do you agree that the angle is the inverse tan of -4/7 ?