1. The problem statement, all variables and given/known data Show that 8sinx + 15cosx ≤ 17 2. Relevant equations 8^2 + 15^2 = 17^2, or (8,15,17) is a Pythagorean triplet Identities like sin^2x + cos^2x = 1 3. 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.