How to find reference angle
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In quadrant II, “ Students,” only sine and its reciprocal function, cosecant, are positive.
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In quadrant I, which is “ A,” all of the six trigonometric functions are positive. To help us remember which of the six trigonometric functions are positive in each quadrant, we can use the mnemonic phrase “All Students Take Calculus” Each of the four words in the phrase corresponds to one of the four quadrants, starting with quadrant I and rotating counterclockwise. Figure 3 shows which functions are positive in which quadrant. The trigonometric function values for the original angle will be the same as those for the reference angle, except for the positive or negative sign, which is determined by x– and y-values in the original quadrant. The sign depends on the quadrant of the original angle. We can find the exact trig value of any angle in any quadrant if we apply the trig function to the reference angle. We will use the reference angle of the angle of rotation combined with the quadrant in which the terminal side of the angle lies.
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They can also be used to find \left(x,y\right) coordinates for those angles. Reference angles make it possible to evaluate trigonometric functions for angles outside the first quadrant.