What is the general solution for 300cos(70)=375cos(θ) ?

The general solution for 300cos(70)=375cos(θ) is θ=1.29364…+360n,θ=360-1.29364…+360n

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300cos(70)=375cos(θ)

300 cos (7 0^{\circ}) = 375 cos (θ)

θ = 1.29364 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 1.29364 \dots + 36 0^{\circ} n

Radians

θ = 1.29364 \dots + 2 πn, θ = 2 π - 1.29364 \dots + 2 πn

Solution steps

300 cos (7 0^{\circ}) = 375 cos (θ)

Switch sides

375 cos (θ) = 300 cos (7 0^{\circ})

Divide both sides by

375

375 cos (θ) = 300 cos (7 0^{\circ})

Divide both sides by

375

\frac{375 cos ( θ )}{375} = \frac{300 cos ( 7 0 ^{\circ} )}{375}

Simplify

cos (θ) = \frac{4 cos ( 7 0 ^{\circ} )}{5}

cos (θ) = \frac{4 cos ( 7 0 ^{\circ} )}{5}

Apply trig inverse properties

cos (θ) = \frac{4 cos ( 7 0 ^{\circ} )}{5}

General solutions for

cos (θ) = \frac{4 cos ( 7 0 ^{\circ} )}{5}

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

θ = arccos (\frac{4 cos ( 7 0 ^{\circ} )}{5}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{4 cos ( 7 0 ^{\circ} )}{5}) + 36 0^{\circ} n

θ = arccos (\frac{4 cos ( 7 0 ^{\circ} )}{5}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{4 cos ( 7 0 ^{\circ} )}{5}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 1.29364 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 1.29364 \dots + 36 0^{\circ} n

812.25 = 399.6001 + 400 - 1140 cos (a)

- 0.6 = sin (2 x)

x, (sin (π x) + cos (π y))^{5} = 36

sin (θ) = - \frac{2}{2}, 0 \leq θ < 2 π

2 sin (\frac{1}{2} x) + 2 = 0

What is the general solution for 300cos(70)=375cos(θ) ?
The general solution for 300cos(70)=375cos(θ) is θ=1.29364…+360n,θ=360-1.29364…+360n