Solve 7 sin ( 3 x ) = 5 for the two smallest positive solutions A and B, with A < B

Question

What is A and B?

A=

B=

Answer 1

sin(3x) = 5/7; 3x = sin^-1(5/7) + 2πn; x = sin^-1(5/7)/3 + 2πn/3;

or 3x = π - sin^-1(5/7) + 2πn, x = π/3 - sin^-1(5/7)/3 + 2πn/3.

Now veraying n we get: A = sin^-1(5/7)/3 = 0.2652 (n = 0) and B = π/3 - sin^-1(5/7)/3 = 0.7820 (n = 0)

Answer 2

Solve for X, which will have two solutions (A and B).

7 sin (3x) = 5

sin (3x) = 5/7

Inverse sin: 3x = 45.6° (Quadrant I of unit circle) as well as 180-45.6 = 134.4° (Quadrant II of unit circle)

x=15.2 (A) and 44.8 (B)