Answer:
Step-by-step explanation:
we would like to solve the following trigonometric equation:
the left hand side can be rewritten using <u>angle </u><u>sum </u><u>indentity</u><u> </u><u>of </u><u>sin </u>which is given by:
therefore Let
Thus substitute:
simplify addition:
keep in mind that <u>sin(</u><u>t)</u><u>=</u><u>sin(</u><u>π-t)</u><u> </u>saying that there're two equation to solve:
take inverse trig and that yields:
add π to both sides of the second equation and that yields:
sin function has a period of <u>2</u><u>n</u><u>π</u><u> </u>thus add the period:
divide I equation by 4 and II by -4 which yields:
recall that,<u>-</u><u>½</u><u>(</u><u>nπ)</u><u>=</u><u>½</u><u>(</u><u>nπ)</u><u> </u>therefore,
by using a calculator we acquire:
hence,
the general solution for: for the trig equation are