What is the general solution for sin(x)-cos(x)= 1/3 ?

The general solution for sin(x)-cos(x)= 1/3 is x=0.23794…+2pin+pi/4 ,x=pi-0.23794…+2pin+pi/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x)-cos(x)= 1/3

sin (x) - cos (x) = \frac{1}{3}

x = 0.23794 \dots + 2 πn + \frac{π}{4}, x = π - 0.23794 \dots + 2 πn + \frac{π}{4}

Solution steps

sin (x) - cos (x) = \frac{1}{3}

Rewrite using trig identities

2 sin (x - \frac{π}{4}) = \frac{1}{3}

Divide both sides by

2

sin (x - \frac{π}{4}) = \frac{2}{6}

Apply trig inverse properties

x - \frac{π}{4} = arcsin (\frac{2}{6}) + 2 πn, x - \frac{π}{4} = π - arcsin (\frac{2}{6}) + 2 πn

Solve

x - \frac{π}{4} = arcsin (\frac{2}{6}) + 2 πn : x = arcsin (\frac{1}{3 2}) + 2 πn + \frac{π}{4}

Solve

x - \frac{π}{4} = π - arcsin (\frac{2}{6}) + 2 πn : x = π - arcsin (\frac{1}{3 2}) + 2 πn + \frac{π}{4}

x = arcsin (\frac{1}{3 2}) + 2 πn + \frac{π}{4}, x = π - arcsin (\frac{1}{3 2}) + 2 πn + \frac{π}{4}

Show solutions in decimal form

x = 0.23794 \dots + 2 πn + \frac{π}{4}, x = π - 0.23794 \dots + 2 πn + \frac{π}{4}

tan^{2} (x) = sec (x) - 1, 0 \leq x \leq 2 π

sin^{2} (θ) = 2 sin^{2} (\frac{θ}{2})

cos (x) = cos (x)

(sec^{2} (x) + 1) (sec^{2} (x) - 1) = tan (x)

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

What is the general solution for sin(x)-cos(x)= 1/3 ?
The general solution for sin(x)-cos(x)= 1/3 is x=0.23794…+2pin+pi/4 ,x=pi-0.23794…+2pin+pi/4