What is the general solution for sin(x)+cos(x)= 2/3 ?

The general solution for sin(x)+cos(x)= 2/3 is x=0.49088…+2pin-pi/4 ,x=pi-0.49088…+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)= 2/3

sin (x) + cos (x) = \frac{2}{3}

x = 0.49088 \dots + 2 πn - \frac{π}{4}, x = π - 0.49088 \dots + 2 πn - \frac{π}{4}

Solution steps

sin (x) + cos (x) = \frac{2}{3}

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = \frac{2}{3}

Divide both sides by

2

sin (x + \frac{π}{4}) = \frac{2}{3}

Apply trig inverse properties

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

Solve

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

Solve

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

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

Show solutions in decimal form

x = 0.49088 \dots + 2 πn - \frac{π}{4}, x = π - 0.49088 \dots + 2 πn - \frac{π}{4}

2 cos^{2} (2 θ) = 1 - cos (2 θ)

1 + tan^{2} (x) = 0

sin (x) = \frac{3}{8}

x, tan (x) + cot (x) = \frac{1}{f}

sec^{2} (x) - 1 + tan (x) - 3 tan (x) = 3

What is the general solution for sin(x)+cos(x)= 2/3 ?
The general solution for sin(x)+cos(x)= 2/3 is x=0.49088…+2pin-pi/4 ,x=pi-0.49088…+2pin-pi/4