True or False Precalculus 127 Question

Question

True or false, sin(u+pi) = sinu +sinpi for all angles u.

Answer 1

False. Think of an angle in the first quadrant. The sine of that angle would be positive if you added that to the sine of pi , which is zero, the answer would still be positive. However, an angle in the first quadrant plus pi would put it in the 3rd quadrant where the sine is negative.

Answer 2

False. If you draw an angle u in quadrant 1 then sin u is some value which we will call x. if you add pi radians (180 degrees) to this then the value for sin of this angle is (-x) Draw it and you will see

Since sin pi=0 sinu+ sinpi= sin u which we called x

x is not equal to (-x)