What is the general solution for sin(x)-cos(x)=0.5 ?

The general solution for sin(x)-cos(x)=0.5 is x=0.36136…+2pin+pi/4 ,x=pi-0.36136…+2pin+pi/4

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sin(x)-cos(x)=0.5

sin (x) - cos (x) = 0.5

x = 0.36136 \dots + 2 πn + \frac{π}{4}, x = π - 0.36136 \dots + 2 πn + \frac{π}{4}

Solution steps

sin (x) - cos (x) = 0.5

Rewrite using trig identities

2 sin (x - \frac{π}{4}) = 0.5

Divide both sides by

2

sin (x - \frac{π}{4}) = 0.35355 \dots

Apply trig inverse properties

x - \frac{π}{4} = arcsin (0.35355 \dots) + 2 πn, x - \frac{π}{4} = π - arcsin (0.35355 \dots) + 2 πn

Solve

x - \frac{π}{4} = arcsin (0.35355 \dots) + 2 πn : x = arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}

Solve

x - \frac{π}{4} = π - arcsin (0.35355 \dots) + 2 πn : x = π - arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}

x = arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}, x = π - arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}

Show solutions in decimal form

x = 0.36136 \dots + 2 πn + \frac{π}{4}, x = π - 0.36136 \dots + 2 πn + \frac{π}{4}

tan (t) = \frac{1}{4}

tan (x) sin (x) + tan (x) = 0

y, tan (x y) = x

cot^{2} (x) - 3 csc (x) + 3 = 0

2 sin^{2} (\frac{θ}{2} - \frac{π}{6}) - 1 = 0

What is the general solution for sin(x)-cos(x)=0.5 ?
The general solution for sin(x)-cos(x)=0.5 is x=0.36136…+2pin+pi/4 ,x=pi-0.36136…+2pin+pi/4