This is not Calculus question.
8 sin x - 9 √2 = 6 sin x - 8 √2
Subtract 6 sin x to both sides
2 sin x - 9 √2 = - 8 √2
Add 9 √2 to both sides
2 sin x = √2
sin x = √2 / 2
On interval 0 to 2 π sin x = √2 / 2 for x = 45° = π / 4 rad
and
x = 135° = 3 / 4 π rad
Period of sin x is 2 π rad so the solutions are:
x = π / 4 + 2 π n
and
x = 3 / 4 π + 2 π n
where
n = ± 1 , ± 2 , ± 3...
By the way √2 / 2 is the same as 1 / √2 becouse:
√2 / 2 = √2 / √2 ∙ √2 = 1 / √2
Find all solutions of the question.
8 sin x - 9sqrt(2) = 6 sin x - 8sqrt(2)
2 answers
My typo.
n = 0 , ± 1 , ± 2 , ± 3...
n = 0 , ± 1 , ± 2 , ± 3...