What is the general solution for cos(θ)= 9/12 ?

The general solution for cos(θ)= 9/12 is θ=0.72273…+2pin,θ=2pi-0.72273…+2pin

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cos(θ)= 9/12

cos (θ) = \frac{9}{12}

θ = 0.72273 \dots + 2 πn, θ = 2 π - 0.72273 \dots + 2 πn

Degrees

θ = 41.40962 \dots^{\circ} + 36 0^{\circ} n, θ = 318.59037 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (θ) = \frac{9}{12}

Cancel the common factor:

3

cos (θ) = \frac{3}{4}

Apply trig inverse properties

cos (θ) = \frac{3}{4}

General solutions for

cos (θ) = \frac{3}{4}

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

θ = arccos (\frac{3}{4}) + 2 πn, θ = 2 π - arccos (\frac{3}{4}) + 2 πn

θ = arccos (\frac{3}{4}) + 2 πn, θ = 2 π - arccos (\frac{3}{4}) + 2 πn

Show solutions in decimal form

θ = 0.72273 \dots + 2 πn, θ = 2 π - 0.72273 \dots + 2 πn

csc (x) + cot (x) = - 1, 0 \leq x \leq 2 π

sin (x) + cos (x) = \frac{5}{7}, 9 0^{\circ} > x > 0^{\circ}

2 cos^{2} (θ) + cos (θ) - 1 = 0, \forall 0 \leq θ < 2 π

2 cos (4 5^{\circ} - x) = 1

sin (θ) = 0.35

What is the general solution for cos(θ)= 9/12 ?
The general solution for cos(θ)= 9/12 is θ=0.72273…+2pin,θ=2pi-0.72273…+2pin