Visual Proof of Sin+Cos Identity

Visual proof for trigonometric identity for sin + cos

You can derive this identity starting from: [math]sin \alpha + cos \alpha = K sin (\alpha + t)[/math] What is the maximum value of [math]sin \alpha + cos \alpha [/math] ? For what value of [math]\alpha[/math] does it occur? What is the maximum value of [math] sin \alpha [/math] ? For what value does it occur?