http://puu.sh/gTVVs.png
Can someone please walk me through how to answer these questions in chapter 6, exercise D.
Thanks in advance.
Well first of all, analyse the given information.
sin(x) = 0.3
So that means the angle 'x' is found within 0 and pi, as sin is positive in this interval.
So for q5, sin(-x) means the exact angle between 0 and pi, but the negative of it, so it is found in either the third or fourth quadrant where sin is negative. So sin(-x) = -0.3 (it's -0.3 because it's the same angle as sin(x) = 0.3, but just the negative of it)
cos(a) = 0.6
We know that cos is only positive in the first and fourth quadrant, so the angle 'a' lies between this interval. Lets try cos(-a).
cos(-a) will produce the same value of cos(a), but the sign may be changed. Say the angle 'a' is in the first quadrant, now we are finding '-a', so now the angle is in the fourth quadrant, where cos is still positive. Same goes with if 'a' is in the fourth quadrant, take the negative of it, we are now in the first quadrant, where cos is still positive. So cos(-a) = 0.6
My word of advice for questions like this, draw a small diagram of the cartesian plane, and actually visualise what you are doing. Draw the angles in the appropiate quadrants! Hope I helped
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