How many solutions are there to the equation 3cosx=sinx on the interval [0, 2π]1236

Thst asked Mar 26, 2023

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Thst asked Mar 26, 2023

by Thst

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8 votes

3 cos x = sin x

Divide each side by cos x

3 cos x / cos x = sin x / cos x

3 = tan x

Take the inverse tan of each side

tan ^-1(3) = tan^-1( tan (x))

Since tan has a period of pi, there are 2 solutions in the interval of [0, 2pi]

Markus Kreth answered Mar 31, 2023

3.5k points

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