Question 968978
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if sine theta = -4/7 and is in quadrant 3, then the sum of sine theta + sine (theta-pie)+sine(2pie+theta) is?
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        This problem allows and assumes much simpler solution comparing with that in the post by @lwsshak3.



<pre>
Second addend, {{{sin(theta-pi)}}}, has the opposite value to the first addend, {{{sin(theta)}}}.

Therefore , when added, these two addends mutually cancel each other, giving 0 (zero).


Thus the sum of the first two addends vanishes, and the given expression is reduced to the last single term

        {{{sin(2*pi + theta)}}},

which, due to the periodicity of function sin, is simply sin(theta), which is -4/7 (given in the problem).


So, the ANSWER to the problem's question is -4/7.
</pre>

Solved in a simple way, without any calculations, using the basic properties of function sin.


I am 127% sure that this is the desired and the expected method of solution to the given problem.