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# solve for d. Help please...

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a)

b)

Guest Dec 14, 2017
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#1
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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.
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
#2
0

a) d= -86.0730091830127585

b) d= -41.8584073464102068

1. *I just used the calculator: web2.0calc.com/
Guest Dec 15, 2017
#3
+81022
+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

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