What is the general solution for 1.6sin(θ)=1.49 ?

The general solution for 1.6sin(θ)=1.49 is θ=1.19782…+2pin,θ=pi-1.19782…+2pin

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1.6sin(θ)=1.49

1.6 sin (θ) = 1.49

θ = 1.19782 \dots + 2 πn, θ = π - 1.19782 \dots + 2 πn

Degrees

θ = 68.63051 \dots^{\circ} + 36 0^{\circ} n, θ = 111.36948 \dots^{\circ} + 36 0^{\circ} n

Solution steps

1.6 sin (θ) = 1.49

Multiply both sides by

100

1.6 sin (θ) = 1.49

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

1.6 sin (θ) \cdot 100 = 1.49 \cdot 100

Refine

160 sin (θ) = 149

160 sin (θ) = 149

Divide both sides by

160

160 sin (θ) = 149

Divide both sides by

160

\frac{160 sin ( θ )}{160} = \frac{149}{160}

Simplify

sin (θ) = \frac{149}{160}

sin (θ) = \frac{149}{160}

Apply trig inverse properties

sin (θ) = \frac{149}{160}

General solutions for

sin (θ) = \frac{149}{160}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

θ = arcsin (\frac{149}{160}) + 2 πn, θ = π - arcsin (\frac{149}{160}) + 2 πn

θ = arcsin (\frac{149}{160}) + 2 πn, θ = π - arcsin (\frac{149}{160}) + 2 πn

Show solutions in decimal form

θ = 1.19782 \dots + 2 πn, θ = π - 1.19782 \dots + 2 πn

cos (x) = 0.695

3 + sec (x) = 5

cos (x) = \frac{3}{30}

- 5 sin (t) + 9 cos (t) = 0

sin (2.5 x) = 2.75 cos (2.5 x)

What is the general solution for 1.6sin(θ)=1.49 ?
The general solution for 1.6sin(θ)=1.49 is θ=1.19782…+2pin,θ=pi-1.19782…+2pin