What is the general solution for sin(x)+cos(x)=0.2 ?

The general solution for sin(x)+cos(x)=0.2 is x=0.14189…+2pin-pi/4 ,x=pi-0.14189…+2pin-pi/4

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sin(x)+cos(x)=0.2

sin (x) + cos (x) = 0.2

x = 0.14189 \dots + 2 πn - \frac{π}{4}, x = π - 0.14189 \dots + 2 πn - \frac{π}{4}

Solution steps

sin (x) + cos (x) = 0.2

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = 0.2

Divide both sides by

2

sin (x + \frac{π}{4}) = 0.14142 \dots

Apply trig inverse properties

x + \frac{π}{4} = arcsin (0.14142 \dots) + 2 πn, x + \frac{π}{4} = π - arcsin (0.14142 \dots) + 2 πn

Solve

x + \frac{π}{4} = arcsin (0.14142 \dots) + 2 πn : x = arcsin (0.14142 \dots) + 2 πn - \frac{π}{4}

Solve

x + \frac{π}{4} = π - arcsin (0.14142 \dots) + 2 πn : x = π - arcsin (0.14142 \dots) + 2 πn - \frac{π}{4}

x = arcsin (0.14142 \dots) + 2 πn - \frac{π}{4}, x = π - arcsin (0.14142 \dots) + 2 πn - \frac{π}{4}

Show solutions in decimal form

x = 0.14189 \dots + 2 πn - \frac{π}{4}, x = π - 0.14189 \dots + 2 πn - \frac{π}{4}

sin (x) cos (x) = - \frac{2}{4}

sin (a) = 0.3

sin (x) = \frac{5}{13}, tan (x), \frac{π}{2} \leq x \leq π

sin (x) + cos^{2} (x) = \frac{5}{4}

2 cos^{2} (θ) - 5 cos (θ) - 3 = 0

What is the general solution for sin(x)+cos(x)=0.2 ?
The general solution for sin(x)+cos(x)=0.2 is x=0.14189…+2pin-pi/4 ,x=pi-0.14189…+2pin-pi/4