What is the general solution for sin(x)+cos(x)= 2/5 ?

The general solution for sin(x)+cos(x)= 2/5 is x=0.28675…+2pin-pi/4 ,x=pi-0.28675…+2pin-pi/4

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sin(x)+cos(x)= 2/5

sin (x) + cos (x) = \frac{2}{5}

x = 0.28675 \dots + 2 πn - \frac{π}{4}, x = π - 0.28675 \dots + 2 πn - \frac{π}{4}

Solution steps

sin (x) + cos (x) = \frac{2}{5}

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = \frac{2}{5}

Divide both sides by

2

sin (x + \frac{π}{4}) = \frac{2}{5}

Apply trig inverse properties

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

Solve

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

Solve

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

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

Show solutions in decimal form

x = 0.28675 \dots + 2 πn - \frac{π}{4}, x = π - 0.28675 \dots + 2 πn - \frac{π}{4}

2 cos (x) + 2 sin (x) cos (x) = 0

100 cos (3 0^{\circ}) - 200 cos (θ) = 0

x, y = sin (2 x + 3 y)

cos (θ) = \frac{8}{9}

2 sin (x) - cos (x) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

What is the general solution for sin(x)+cos(x)= 2/5 ?
The general solution for sin(x)+cos(x)= 2/5 is x=0.28675…+2pin-pi/4 ,x=pi-0.28675…+2pin-pi/4