Solve 3=8+5 cos((180 x-180) /6)

Evaluate

3 = 8 + 5 cos (\frac{180 x - 180}{6})

Divide the terms

More Steps

3 = 8 + 5 cos (30 x - 30)

Swap the sides of the equation

8 + 5 cos (30 x - 30) = 3

Move the constant to the right-hand side and change its sign

5 cos (30 x - 30) = 3 - 8

Subtract the numbers

5 cos (30 x - 30) = - 5

Divide both sides

\frac{5 cos ( 30 x - 30 )}{5} = \frac{- 5}{5}

Divide the numbers

cos (30 x - 30) = \frac{- 5}{5}

Divide the numbers

More Steps

cos (30 x - 30) = - 1

Use the inverse trigonometric function

30 x - 30 = arccos (- 1)

Calculate

30 x - 30 = π

Add the period of 2 kπ, k \in Z to find all solutions

30 x - 30 = π + 2 kπ, k \in Z

Solution

More Steps

x = \frac{π + 30}{30} + \frac{kπ}{15}, k \in Z

Alternative Form

x \approx 63.2957 8^{\circ} + 1 2^{\circ} k, k \in Z

Alternative Form

x \approx 1.10472 + \frac{kπ}{15}, k \in Z

Solve the equation