Trigonometric Equation

Geometry Level 4

Given that 0 ∘ ≤ θ ≤ 36 0 ∘ 0^{\circ}\leq\theta\leq 360^{\circ} satisfies the trigonometric equation

5 sin ⁡ θ cos ⁡ 2 θ + 2 cos ⁡ θ = 0 , 5\sin\theta\cos^2\theta+2\cos\theta=0,

find the number of values θ \theta can take.


The answer is 6.

Victor Loh by Victor Loh , 19, Singapore

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2 solutions

Nathanael Case
Jul 25, 2015

I googled "y=5sin(x)(cos(x))^2+2cos(x)" so that it will draw a graph for me, then I counted the x-intercepts.

Muahahah >:)

:p

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Akhilesh Singh
Sep 3, 2014

The above equation will break into two independent equations.the first equation is cos(a)=0 with 0 <=a<=360.the possible values of a are a=90,270(in degrees) i.e., 2 values. The second equation will be sin(b)=-0.8 with 0<=b<=720. The possible values of b are 233.13,306.87,593.13,666.87(all in degrees),i.e., 4 values.So the ans is 2+4=6.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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