All solutions to equation write answer in radians in terms of pi2cos(theta) - √(2) = 0

Question

All solutions to equation

write answer in radians in terms of pi
`2cos(theta) - √(2) = 0`

Answer 1

To solve the equation
`2\cos(\theta) - √(2) = 0\\` and express the answer in radians in terms of π, we can follow these steps:

Step 1: Add
`√(2)\\` to both sides of the equation:

`2\cos(\theta) = √(2)\\`

Step 2: Divide both sides of the equation by 2:

`\cos(\theta) = (√(2))/(2)\\`

Step 3: Recall the special values of cosine in the first quadrant:

`\cos(\theta) = (√(2))/(2)\\`¥ corresponds to
`\\ \theta = (\pi)/(4)\\` in radians.

Therefore, the solution to the equation in radians in terms of π is
`\theta = (\pi)/(4)\\`.