Trigonometry equation?

Question

Hi, Could someone help me solve this equation?

sin(5x + pi/8) = sin (3x + pi/4) ? How do I solve it?

Answer 1

Remember that sin (π - A) = sin A

Let's go back to the general equation:

sinX = sinA

This equation is equivalent to 2 algebraic equations:

(a) X = A +k 2π

(b) X = (π - A) + k 2π

sin(5x + π/8) = sin (3x + π/4)

(a) 5x + π/8 = 3x + π/4 + k 2π

2x = π/8 + k 2π

. x = π/16 + kπ

(b) 5x + π/8 = π - (3x + π/4) + k 2π

8x = 5π/8 + k 2π

. x = 5π/64 + k π/4

The solutions to sin(5x + π/8) = sin (3x + π/4) are

x1 = π/16 + kπ and x2 = 5π/64 + k π/4

Answer 2

Then 5x-3x=pi/4-pi/8, 2x=pi/8,x=pi/16 & pi/16+pi/2,&pi/16+pi,and

pi/16+3pi/2 etc.

Answer 3

Because both sides are sin you just remove it like you would any other function.

5x + pi/8 = 3x + pi/4