What is the general solution for 28cos(θ)=4,0<= θ<360 ?

The general solution for 28cos(θ)=4,0<= θ<360 is θ=1.42744…,θ=360-1.42744…

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28cos(θ)=4,0<= θ<360

28 cos (θ) = 4, 0^{\circ} \leq θ < 36 0^{\circ}

θ = 1.42744 \dots, θ = 36 0^{\circ} - 1.42744 \dots

Radians

θ = 1.42744 \dots, θ = 2 π - 1.42744 \dots

Solution steps

28 cos (θ) = 4, 0^{\circ} \leq θ < 36 0^{\circ}

Divide both sides by

28

28 cos (θ) = 4

Divide both sides by

28

\frac{28 cos ( θ )}{28} = \frac{4}{28}

Simplify

cos (θ) = \frac{1}{7}

cos (θ) = \frac{1}{7}

Apply trig inverse properties

cos (θ) = \frac{1}{7}

General solutions for

cos (θ) = \frac{1}{7}

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

θ = arccos (\frac{1}{7}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{1}{7}) + 36 0^{\circ} n

θ = arccos (\frac{1}{7}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{1}{7}) + 36 0^{\circ} n

Solutions for the range

0 \leq θ < 36 0^{\circ}

θ = arccos (\frac{1}{7}), θ = 36 0^{\circ} - arccos (\frac{1}{7})

Show solutions in decimal form

θ = 1.42744 \dots, θ = 36 0^{\circ} - 1.42744 \dots

6 sin (θ) + 2 = sin (θ)

cos (θ) = - \frac{19}{17}

5 = 7 - cos (θ) + 5 cos (2 θ)

tan (2 x) = 0.32

sin (x) = \frac{- 3}{2}, 27 0^{\circ} < x < 36 0^{\circ}

What is the general solution for 28cos(θ)=4,0<= θ<360 ?
The general solution for 28cos(θ)=4,0<= θ<360 is θ=1.42744…,θ=360-1.42744…