What is the general solution for 1500=250*8*cos(θ) ?

The general solution for 1500=250*8*cos(θ) is θ=0.72273…+2pin,θ=2pi-0.72273…+2pin

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1500=2508cos(θ)

1500 = 250 \cdot 8 \cdot cos (θ)

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

1500 = 250 \cdot 8 cos (θ)

Switch sides

250 \cdot 8 cos (θ) = 1500

Divide both sides by

2000

250 \cdot 8 cos (θ) = 1500

Divide both sides by

2000

\frac{250 \cdot 8 cos ( θ )}{2000} = \frac{1500}{2000}

Simplify

cos (θ) = \frac{3}{4}

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

- sin (2 x) = sin (4 x)

sin (x) = - 0.61

2 cos (3 x) + 2 = 0

cos (2 x) - sin (- x) = 0

sin (x) cos (x) = \frac{1}{2} cos (x)

What is the general solution for 1500=250*8*cos(θ) ?
The general solution for 1500=250*8*cos(θ) is θ=0.72273…+2pin,θ=2pi-0.72273…+2pin