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

The general solution for cos(x)-sin(x)=0.5 is x= pi/4+2pin-0.36136…,x=(5pi)/4+2pin+0.36136…

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cos(x)-sin(x)=0.5

cos (x) - sin (x) = 0.5

x = \frac{π}{4} + 2 πn - 0.36136 \dots, x = \frac{5 π}{4} + 2 πn + 0.36136 \dots

Solution steps

cos (x) - sin (x) = 0.5

Subtract

0.5

from both sides

cos (x) - sin (x) - 0.5 = 0

Rewrite using trig identities

- 0.5 - 1.41421 \dots sin (\frac{4 x - π}{4}) = 0

Move

0.5

to the right side

- 1.41421 \dots sin (\frac{4 x - π}{4}) = 0.5

Divide both sides by

- 1.41421 \dots

sin (\frac{4 x - π}{4}) = - 0.35355 \dots

Apply trig inverse properties

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

Solve

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

Solve

\frac{4 x - π}{4} = π + arcsin (0.35355 \dots) + 2 πn : x = \frac{5 π}{4} + 2 πn + arcsin (0.35355 \dots)

x = \frac{π}{4} + 2 πn - arcsin (0.35355 \dots), x = \frac{5 π}{4} + 2 πn + arcsin (0.35355 \dots)

Show solutions in decimal form

x = \frac{π}{4} + 2 πn - 0.36136 \dots, x = \frac{5 π}{4} + 2 πn + 0.36136 \dots

sin (x + π) - sin (x) + 3 = 0

csc (x) = 1.5

tan (t) = 0

cos (\frac{θ}{2}) = \frac{1}{2}

\frac{2}{3} cos (3 θ) = 1

What is the general solution for cos(x)-sin(x)=0.5 ?
The general solution for cos(x)-sin(x)=0.5 is x= pi/4+2pin-0.36136…,x=(5pi)/4+2pin+0.36136…