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Popular Trigonometry >

9.68^2=12.5^2+6.47^2-212.56.47*cos(θ)

Solution

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

Solution

θ = 0.86912 \dots + 2 πn, θ = 2 π - 0.86912 \dots + 2 πn

+1

Degrees

θ = 49.79734 \dots^{\circ} + 36 0^{\circ} n, θ = 310.20265 \dots^{\circ} + 36 0^{\circ} n

Solution steps

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

Switch sides

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

Multiply the numbers:

2 \cdot 12.5 \cdot 6.47 = 161.75

12. 5^{2} + 6.4 7^{2} - 161.75 cos (θ) = 9.6 8^{2}

12. 5^{2} = 156.25

156.25 + 6.4 7^{2} - 161.75 cos (θ) = 9.6 8^{2}

6.4 7^{2} = 41.8609

156.25 + 41.8609 - 161.75 cos (θ) = 9.6 8^{2}

Add the numbers:

156.25 + 41.8609 = 198.1109

- 161.75 cos (θ) + 198.1109 = 9.6 8^{2}

9.6 8^{2} = 93.7024

- 161.75 cos (θ) + 198.1109 = 93.7024

Move

198.1109

to the right side

- 161.75 cos (θ) + 198.1109 = 93.7024

Subtract

198.1109

from both sides

- 161.75 cos (θ) + 198.1109 - 198.1109 = 93.7024 - 198.1109

Simplify

- 161.75 cos (θ) = - 104.4085

- 161.75 cos (θ) = - 104.4085

Divide both sides by

- 161.75

- 161.75 cos (θ) = - 104.4085

Divide both sides by

- 161.75

\frac{- 161.75 cos ( θ )}{- 161.75} = \frac{- 104.4085}{- 161.75}

Simplify

cos (θ) = \frac{104.4085}{161.75}

cos (θ) = \frac{104.4085}{161.75}

Apply trig inverse properties

cos (θ) = \frac{104.4085}{161.75}

General solutions for

cos (θ) = \frac{104.4085}{161.75}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

θ = arccos (\frac{104.4085}{161.75}) + 2 πn, θ = 2 π - arccos (\frac{104.4085}{161.75}) + 2 πn

θ = arccos (\frac{104.4085}{161.75}) + 2 πn, θ = 2 π - arccos (\frac{104.4085}{161.75}) + 2 πn

Show solutions in decimal form

θ = 0.86912 \dots + 2 πn, θ = 2 π - 0.86912 \dots + 2 πn

Graph

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