#1**0 **

Solve for d:

1 = sin(d - π/4)

Reverse the equality in 1 = sin(d - π/4) in order to isolate d to the left hand side.

1 = sin(d - π/4) is equivalent to sin(d - π/4) = 1:

sin(d - π/4) = 1

Eliminate the sine from the left hand side.

Take the inverse sine of both sides:

d - π/4 = 2 π n + π/2 for n element Z

Solve for d.

Add π/4 to both sides:

**d = 2 π n + (3 π)/4 for n element Z**

Solve for d:

1 = sin(2 (π - d))

Reverse the equality in 1 = sin(2 (π - d)) in order to isolate d to the left hand side.

1 = sin(2 (π - d)) is equivalent to sin(2 (π - d)) = 1:

sin(2 (π - d)) = 1

Eliminate the sine from the left hand side.

Take the inverse sine of both sides:

2 (π - d) = 2 π n + π/2 for n element Z

Divide both sides by a constant to simplify the equation.

Divide both sides by 2:

π - d = π n + π/4 for n element Z

Isolate terms with d to the left-hand side.

Subtract π from both sides:

-d = π n - (3 π)/4 for n element Z

Solve for d.

Multiply both sides by -1:

**d = (3 π)/4 - π n for n element Z**

Guest Dec 14, 2017

#3**+1 **

1 = sin (5pi/4 - d)

arcsin 1 = arcsin [ sin (5pi/4 - d) ]

pi/2 = 5pi/4 - d

d = 5pi/4 - pi/2

d = 5pi/4 - 2pi/4

d = 3pi/4 + n* 2pi where n is an integer

1 = sin [ 2 (pi -d)]

arcsin 1 = arcsin [sin [2(pi - d ) ]

pi/2 = 2 (pi - d) divide both sides by 2

pi/4 = pi - d

d = pi - pi/4

d = 3pi/4 + n * 2 pi where n is an integer

CPhill Dec 15, 2017