- #1

Bearded Man

- 38

- 0

## Homework Statement

Show that 8sinx + 15cosx ≤ 17

## Homework Equations

8^2 + 15^2 = 17^2, or (8,15,17) is a Pythagorean triplet

Identities like sin^2x + cos^2x = 1

## The Attempt at a Solution

8sinx + 15cosx <= y

square both sides, clean up

64sin^2x + 240sinxcosx + 225cos^2x ≤y^2

substitute sin^2x for 1-cos^2x and likewise for cos^2x, derived from Pythagorean Identity.

289 - 64cos^2x -225sin^2x +240sinxcosx ≤ y^2

I need to show that the trigonometric functions on the left side equal 0, so I can take the square root of both sides and find 17≤ y, but I don't know how to do that. It is also possible that I'm approaching this from the wrong viewpoint.