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Popular >

17sin(θ+61.9)=k

Solution

17 sin (θ + 61. 9^{\circ}) = k

Solution

θ = arcsin (\frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}, θ = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

+1

Radians

θ = arcsin (\frac{k}{17}) - \frac{619 π}{1800} + 2 πn, θ = π + arcsin (- \frac{k}{17}) - \frac{619 π}{1800} + 2 πn

Solution steps

17 sin (θ + 61. 9^{\circ}) = k

Divide both sides by

17

17 sin (θ + 61. 9^{\circ}) = k

Divide both sides by

17

\frac{17 sin ( θ + 61. 9 ^{\circ} )}{17} = \frac{k}{17}

Simplify

sin (θ + 61. 9^{\circ}) = \frac{k}{17}

sin (θ + 61. 9^{\circ}) = \frac{k}{17}

Apply trig inverse properties

sin (θ + 61. 9^{\circ}) = \frac{k}{17}

General solutions for

sin (θ + 61. 9^{\circ}) = \frac{k}{17}

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

θ + 61. 9^{\circ} = arcsin (\frac{k}{17}) + 36 0^{\circ} n, θ + 61. 9^{\circ} = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n

θ + 61. 9^{\circ} = arcsin (\frac{k}{17}) + 36 0^{\circ} n, θ + 61. 9^{\circ} = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n

Solve

θ + 61. 9^{\circ} = arcsin (\frac{k}{17}) + 36 0^{\circ} n : θ = arcsin (\frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

θ + 61. 9^{\circ} = arcsin (\frac{k}{17}) + 36 0^{\circ} n

Move

61. 9^{\circ}

to the right side

θ + 61. 9^{\circ} = arcsin (\frac{k}{17}) + 36 0^{\circ} n

Subtract

61. 9^{\circ}

from both sides

θ + 61. 9^{\circ} - 61. 9^{\circ} = arcsin (\frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

Simplify

θ = arcsin (\frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

θ = arcsin (\frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

Solve

θ + 61. 9^{\circ} = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n : θ = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

θ + 61. 9^{\circ} = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n

Move

61. 9^{\circ}

to the right side

θ + 61. 9^{\circ} = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n

Subtract

61. 9^{\circ}

from both sides

θ + 61. 9^{\circ} - 61. 9^{\circ} = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

Simplify

θ = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

θ = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

θ = arcsin (\frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}, θ = 18 0^{\circ} + arcsin (- \frac{k}{17}) + 36 0^{\circ} n - 61. 9^{\circ}

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