Manipulation Or Graphs

Geometry Level 3

{ y = ∣ sin ⁡ x ∣ x 2 + y 2 = 1 \begin{cases} y = \lvert \sin x \rvert \\ x^2+y^2=1 \end{cases}

Find the number of solutions ( x , y ) (x,y) satisfying the system of equations above.

3 1 2 4

Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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1 solution

Tran Quoc Dat
Apr 18, 2016

{ y = ∣ sin ⁡ x ∣ x 2 + y 2 = 1 ⇒ x 2 + sin ⁡ 2 x = 1 ⇒ x 2 = c o s 2 x ⇒ x = ± cos ⁡ x \begin{cases} y=\lvert \sin x \rvert \\ x^2+y^2=1 \end{cases} \Rightarrow x^2+\sin^2 x=1 \Rightarrow x^2 = cos^2 x \Rightarrow x=\pm \cos x . Each equation gives us 1 solution. So, there are 2 solutions in total.

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