Question

The maximum value of sinx + cosx is ____________.

Options

• `sqrt2`

• 1

• `1/sqrt2`

• 2

Answer 1

The maximum value of sinx + cosx is `underline(sqrt2)`.

Explanation:

Since the sine and cosine functions have a range of [-1,1], However, because sine is a rising function and cosine is a decreasing function, the maximum that both can achieve is 45°

`(1/sqrt2) + (1/sqrt2) = sqrt2`