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
+128473 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
