Find value of "x"sin(7x-20°) = cos(3x+40°)

x = 36°n + 7° OR x = 90°n + 37.5° for any integer n

Step-by-step explanation:

Since cos(x) = sin(90°-x),  we have

sin(7x-20°) = sin(90°-(3x+40°)) = sin( 50° - 3x )

sin( x ) = sin( y ) implies either:

x = 360° n + y

or

x = 360°n + 180° - y

Generally sin(x) = sin(y) ⇒ x = 180°n + (-1)ⁿ y

First case:

7x - 20° = 360°n + 50° - 3x

10x = 360°n + 70°

x = 36°n + 7°

Second case:

7x - 20° = 360°n + 180° - ( 50°-3x )

7x - 20° = 360°n + 180° - 50° + 3x

7x - 20° = 360°n + 130° + 3x

4x - 20° = 360°n + 130°

4x = 360°n + 150°

x = 90°n + 37.5°

c. 1,233 miles