Question

Solve the given equation and indicate the number of values of θ sach that 0≤θ<2π ,that satisfy the iquation;
Sin3a+sina=0

Answer 1

Perhaps this identity will help:
\[\sin(a) + \sin(3a) = 4 \cos(a)^{2}\sin(a)\]
sin^2 + cos^==1

a={0,Pi/2}

Answer 2

This is a question with multiple choice of answers.
In this problems they are ranging from 0 to 8.
Which one is right?
Thank you for you help!

Answer 3

First of all, sin^2 + cos^==1 should have been posted as follows:
\[\sin(a)^2+\cos(a)^2=1\]
The problem statement is: "the sine of three times the angle "a" added to the sine of the same angle "a" is equal to zero."

There are restrictions attached to the angle "a". The symbol in the restriction statement, that looks like the symbol "8", is the greek character "theta", a symbol that is interpreted by most experienced math folks as "angle". The person who created the problem should have used "a" rather than theta in the context of this problem and the experience level of the problem solver.

What the restriction statement is saying is that only the solution angle values that are equal to or greater than zero and at the same time less than the angle 2 Pi (360 degrees) should be presented as equation solutions for a. For instance any negative angles that are solutions to the equation, although valid, should not be presented.

I hope this answers you questions.