What is the general solution for cos(θ)= 60/78 ?

The general solution for cos(θ)= 60/78 is θ=0.69315…+2pin,θ=2pi-0.69315…+2pin

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cos(θ)= 60/78

cos (θ) = \frac{60}{78}

θ = 0.69315 \dots + 2 πn, θ = 2 π - 0.69315 \dots + 2 πn

Degrees

θ = 39.71513 \dots^{\circ} + 36 0^{\circ} n, θ = 320.28486 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (θ) = \frac{60}{78}

Cancel the common factor:

6

cos (θ) = \frac{10}{13}

Apply trig inverse properties

cos (θ) = \frac{10}{13}

General solutions for

cos (θ) = \frac{10}{13}

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

θ = arccos (\frac{10}{13}) + 2 πn, θ = 2 π - arccos (\frac{10}{13}) + 2 πn

θ = arccos (\frac{10}{13}) + 2 πn, θ = 2 π - arccos (\frac{10}{13}) + 2 πn

Show solutions in decimal form

θ = 0.69315 \dots + 2 πn, θ = 2 π - 0.69315 \dots + 2 πn

18 sin^{2} (x) = 9

x, sin (x) = cos (y)

2 - 2 sin^{2} (\frac{x}{2}) = 2 cos^{2} (x)

2 cos (x) + 2 sin (x) = 6

6 tan (θ) + 1 = 0

What is the general solution for cos(θ)= 60/78 ?
The general solution for cos(θ)= 60/78 is θ=0.69315…+2pin,θ=2pi-0.69315…+2pin