What is the general solution for sin(45)=1.57*sin(θ) ?

The general solution for sin(45)=1.57*sin(θ) is θ=0.46719…+360n,θ=180-0.46719…+360n

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(45)=1.57*sin(θ)

sin (4 5^{\circ}) = 1.57 \cdot sin (θ)

θ = 0.46719 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.46719 \dots + 36 0^{\circ} n

Radians

θ = 0.46719 \dots + 2 πn, θ = π - 0.46719 \dots + 2 πn

Solution steps

sin (4 5^{\circ}) = 1.57 sin (θ)

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2}

\frac{2}{2} = 1.57 sin (θ)

Switch sides

1.57 sin (θ) = \frac{2}{2}

Multiply both sides by

100

1.57 sin (θ) = \frac{2}{2}

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

1.57 sin (θ) \cdot 100 = \frac{2}{2} \cdot 100

Refine

157 sin (θ) = 502

157 sin (θ) = 502

Divide both sides by

157

157 sin (θ) = 502

Divide both sides by

157

\frac{157 sin ( θ )}{157} = \frac{50 2}{157}

Simplify

sin (θ) = \frac{50 2}{157}

sin (θ) = \frac{50 2}{157}

Apply trig inverse properties

sin (θ) = \frac{50 2}{157}

General solutions for

sin (θ) = \frac{50 2}{157}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

θ = arcsin (\frac{50 2}{157}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{50 2}{157}) + 36 0^{\circ} n

θ = arcsin (\frac{50 2}{157}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{50 2}{157}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.46719 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.46719 \dots + 36 0^{\circ} n

\frac{2}{3} = sec (x)

3 (cos (x) - 1) = - 1

9.6 8^{2} = 12. 5^{2} + 6.4 7^{2} - 2 \cdot 12.5 \cdot 6.47 \cdot cos (θ)

- 4 = \frac{sin ( θ )}{cos ( θ )}

3 = cos (θ)

What is the general solution for sin(45)=1.57*sin(θ) ?
The general solution for sin(45)=1.57*sin(θ) is θ=0.46719…+360n,θ=180-0.46719…+360n