Exercise: Calculate the sign of cos(-302°) and sin(-302°).
We can know the sign of the trigonometric value of an angle depending on which quadrant the angle is located. In the case of cosine and sine, we have the following rules:
Let's calculate the sign of cos(-302°) first. Note that the angle within the cosine is negative; this means that it must be measured from the x-axis clockwise. Now, every quadrant has a total measure of 90°; then, dividing 302 by 90 we obtain
[tex]\frac{302}{90}\approx3.4,[/tex]which means that -302° goes through two complete quadrants and a partial part of a third one. Since we must measure the angle clockwise, -302 lies in the first quadrant.
By the diagram above, the sign of -302° is +.
On the other hand, looking at the sine diagram, we see that the sign of sine(-302°) is + as well.
AnswerThe signs of cos(-302°) and sin(-302°) are both +.
