What is the general solution for cos(θ)=(800cos(70))/(425) ?

The general solution for cos(θ)=(800cos(70))/(425) is θ=0.87133…+360n,θ=360-0.87133…+360n

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cos(θ)=(800cos(70))/(425)

cos (θ) = \frac{800 cos ( 7 0 ^{\circ} )}{425}

θ = 0.87133 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 0.87133 \dots + 36 0^{\circ} n

Radians

θ = 0.87133 \dots + 2 πn, θ = 2 π - 0.87133 \dots + 2 πn

Solution steps

cos (θ) = \frac{800 cos ( 7 0 ^{\circ} )}{425}

Cancel the common factor:

25

cos (θ) = \frac{32 cos ( 7 0 ^{\circ} )}{17}

Apply trig inverse properties

cos (θ) = \frac{32 cos ( 7 0 ^{\circ} )}{17}

General solutions for

cos (θ) = \frac{32 cos ( 7 0 ^{\circ} )}{17}

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

θ = arccos (\frac{32 cos ( 7 0 ^{\circ} )}{17}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{32 cos ( 7 0 ^{\circ} )}{17}) + 36 0^{\circ} n

θ = arccos (\frac{32 cos ( 7 0 ^{\circ} )}{17}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{32 cos ( 7 0 ^{\circ} )}{17}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.87133 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 0.87133 \dots + 36 0^{\circ} n

csc^{(2)} (x) - cot (x) = 2, 0 <, x < 360

2 sin (x) + \frac{3}{4} = \frac{3}{2}

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

20 = 27 sin (x) - 1.5 cos (x)

- 3 sin (θ) = 0

What is the general solution for cos(θ)=(800cos(70))/(425) ?
The general solution for cos(θ)=(800cos(70))/(425) is θ=0.87133…+360n,θ=360-0.87133…+360n