Whats the trig function of cos 315(degrees)?

Trig identity: cos(A)=cos(-A) and the fact that 315d = -45d then cos(315)=cos(-45)=cos(45)= sqrt(2)/2. Approx. .707

Draw an X=Y coordinate system. Draw an angle in the first quadrant. label a point on the terminal side (X,Y) and draw the X and Y sides to the point. The hypotenuse is R (from Pythagoras) and is always positive. Now define the trig functions in terms of X, Y, and R: sin A = Y/R cos A = X/R Tan A = Y/X The reciprocals, csc, sec, and cot are defined the same way. As long as the angle is in the standard position (at the origin and opening counterclockwise for positive angles) these definitions take care of the SIGN of a trig function in any quadrant. 315 degrees is between 270 and 360 - in the 4th quadrant. The REFERENCE ANGLE (the smallest angle between the terminal side (R) and the X=axis) is 45 degrees. Cos 315 is still X/R, the R is always positive and in the 4th quadrant so is the X. Try angles in different quadrants and you'll see the sign of the trig functions change with the + or - sides of the X and Y axes. If you learn the definitions this way it will save you some rethinking when you get to math analysis. It's handy to know the trig functions of the 45-45-90 and 30-60-90 triangles, too. You'll be seeing a lot of them.