Question

Draw a right triangle having hypotenuse of length 6.3cm and one of the acute angle of measure 60°

Answer 1

Hey there,

We want to maximize 12 (sinθ+cosθ) 12 (sin⁡θ+cos⁡θ) . So we want to maximize sinθ+cosθsin⁡θ+cos⁡θ .

Equivalently, we want to maximize (sinθ+cosθ)2(sin⁡θ+cos⁡θ)2 . So we want to maximize sin2θ+cos2θ+2sinθcosθsin2⁡θ+cos2⁡θ+2sin⁡θcos⁡θ .

So we want to maximize sin2θsin⁡2θ . This happens when 2θ=π22θ=π2 .

Hope this helps!