What is the general solution for sin(θ)+cos(θ)=0.46 ?

The general solution for sin(θ)+cos(θ)=0.46 is θ=0.33129…+2pin-pi/4 ,θ=pi-0.33129…+2pin-pi/4

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sin(θ)+cos(θ)=0.46

sin (θ) + cos (θ) = 0.46

θ = 0.33129 \dots + 2 πn - \frac{π}{4}, θ = π - 0.33129 \dots + 2 πn - \frac{π}{4}

Solution steps

sin (θ) + cos (θ) = 0.46

Rewrite using trig identities

2 sin (θ + \frac{π}{4}) = 0.46

Divide both sides by

2

sin (θ + \frac{π}{4}) = 0.32526 \dots

Apply trig inverse properties

θ + \frac{π}{4} = arcsin (0.32526 \dots) + 2 πn, θ + \frac{π}{4} = π - arcsin (0.32526 \dots) + 2 πn

Solve

θ + \frac{π}{4} = arcsin (0.32526 \dots) + 2 πn : θ = arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}

Solve

θ + \frac{π}{4} = π - arcsin (0.32526 \dots) + 2 πn : θ = π - arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}

θ = arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}, θ = π - arcsin (0.32526 \dots) + 2 πn - \frac{π}{4}

Show solutions in decimal form

θ = 0.33129 \dots + 2 πn - \frac{π}{4}, θ = π - 0.33129 \dots + 2 πn - \frac{π}{4}

3 cos (x) - 4 sin (x) = 5

cos (2 x) + 2 cos (x) = - 1

2 cos (x - \frac{π}{4}) - 1 = 0

t, sin (t) + cos (2 t) = 0.75

0 = 3 cos (x)

What is the general solution for sin(θ)+cos(θ)=0.46 ?
The general solution for sin(θ)+cos(θ)=0.46 is θ=0.33129…+2pin-pi/4 ,θ=pi-0.33129…+2pin-pi/4