My Third Problem

Geometry Level pending

s i n x = 3 y sinx=3y

c o s x = 4 y cosx=4y

These simultaneous equations have two solutions for y.

What is their product?


The answer is -0.04.

Daniel Ellesar by Daniel Ellesar , 24, United Kingdom

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1 solution

Daniel Ellesar
Jan 26, 2015

Draw a triangle, where sinx is 3y and cosx is 4y.

Using Pythagoras we find that 9 y 2 + 16 y 2 = 1 9y^{2} + 16y^{2} = 1

y 2 = 1 25 y^{2} = \frac{1}{25}

y = 1 5 y = \frac{1}{5}

y = − 1 5 y = - \frac{1}{5}

0.2 × − 0.2 = − 0.04 0.2 \times -0.2 = -0.04

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