What is the general solution for sin(x)+cos(x)=1.2 ?

The general solution for sin(x)+cos(x)=1.2 is x=1.01319…+2pin-pi/4 ,x=pi-1.01319…+2pin-pi/4

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sin(x)+cos(x)=1.2

sin (x) + cos (x) = 1.2

x = 1.01319 \dots + 2 πn - \frac{π}{4}, x = π - 1.01319 \dots + 2 πn - \frac{π}{4}

Solution steps

sin (x) + cos (x) = 1.2

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = 1.2

Divide both sides by

2

sin (x + \frac{π}{4}) = 0.84852 \dots

Apply trig inverse properties

x + \frac{π}{4} = arcsin (0.84852 \dots) + 2 πn, x + \frac{π}{4} = π - arcsin (0.84852 \dots) + 2 πn

Solve

x + \frac{π}{4} = arcsin (0.84852 \dots) + 2 πn : x = arcsin (0.84852 \dots) + 2 πn - \frac{π}{4}

Solve

x + \frac{π}{4} = π - arcsin (0.84852 \dots) + 2 πn : x = π - arcsin (0.84852 \dots) + 2 πn - \frac{π}{4}

x = arcsin (0.84852 \dots) + 2 πn - \frac{π}{4}, x = π - arcsin (0.84852 \dots) + 2 πn - \frac{π}{4}

Show solutions in decimal form

x = 1.01319 \dots + 2 πn - \frac{π}{4}, x = π - 1.01319 \dots + 2 πn - \frac{π}{4}

30 cos (30 x) + 14 = - 16

x, cot (- x) cos (- x) + sin (- x) = - \frac{1}{f}

cos (x) = - \frac{2}{3}

10 cos^{2} (x) + 5 cos (x) - 5 = 0

2 sin (x) = - 3

What is the general solution for sin(x)+cos(x)=1.2 ?
The general solution for sin(x)+cos(x)=1.2 is x=1.01319…+2pin-pi/4 ,x=pi-1.01319…+2pin-pi/4