Question

Please help on some trigonometry, it would be greatly appreciated!
How to solve this equation?

Answer 1

\[\sin (3\theta) = -1\]

Answer 2

can you slove this?
sin x = -1

Answer 3

yeah, that would be 3pi/2

Answer 4

now
make the substitution
\(3\theta =x \)

Answer 5

\(\theta = ?\)

Answer 6

3pi/6

Answer 7

yes,
look at the fraction 3pi/6
you can simplify it further

Answer 8

pi/2

Answer 9

yep

Answer 10

What we can learn from this is pretty much that whenever solving a trigonometric equation and the given form does not fit in any of the trigonometric entities or equalities then we MUST make a change of variable in order to make it fit and later on solve for the original variable.