A geometry problem by sai aryanreddy

Geometry Level 3

$\sqrt{\sin^{2} \theta}+\sqrt{\cos^{4} \theta} = 1$ Find the number of solutions for $\theta$ in the equation above if $0 \leq \theta \leq 2\pi$

none of these 2 5 3 4 1

1 solution

Rwit Panda
Nov 1, 2015

When we simplify this thing, we need to remember that √x² =|x| and not x.

So, √sin ²¢ = |sin¢| and √cos ⁴¢ = |cos²¢|= |1-sin ²¢|= 1-sin ²¢. {As it is already positive.

So, |sin¢| + 1-sin ²¢=1. |sin¢|=sin ²¢.

Case 1, Sin¢=sin²¢ or sin¢=0,1.

Case 2, Sin ¢=-sin ²¢ or sin ¢=0,-1.

Now, for 0,1,-1, ¢ angle can have infinite values, and no specific range is mentioned. So correct option would be none of these. :)

good solution but by seeing we can say that it has infinite solutions because no range is mentioned

sai aryanreddy - 5 years, 7 months ago

Ya absolutely correct. I just solved the equation for anyone who is not able to do so. Otherwise, for the sake of the problem, we just could have concluded the answer. :)

Rwit Panda - 5 years, 7 months ago

A geometry problem by sai aryanreddy

1 solution

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