MATH SOLVE

3 months ago

Q:
# How do you determine whether the sign of a trigonometric function is positive or negative when dealing with half angles?

Accepted Solution

A:

Explanation:Consider the quadrant of the original angle and where half that angle would lie.Half of any positive 1st- or 2nd-quadrant angle will lie in the first quadrant.Half of any positive 3rd- or 4th-quadrant angle will lie in the second quadrant.___Half of any negative 1st- or 2nd-quadrant angle will lie in the third quadrant.Half of any negative 3rd- or 4th-quadrant angle will lie in the fourth quadrant.___Here, we are using the wording "x-quadrant angle" to mean an angle whose terminal ray lies in the x-quadrant. The measure of that angle may be positive or negative. (Half of -5Ο/4 radians will have different trig function values than half of +3Ο/4 radians, even though they both have their terminal ray in the 2nd quadrant.)We are assuming the angle does not exceed 360Β° (or 2Ο radians). If it does, you need to adjust the half-angle quadrant accordingly.