ShanelleN261501 ShanelleN261501

31-10-2022
Mathematics

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

How many solutions are there to the equation 3cosxsinx on the interval 0 2π1236 class=

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RayH31381 RayH31381

31-10-2022

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]

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