Solve the equation sinx*cos150=0,5-cosx*sin150 if 0<x<360.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

You have not provided a proper question. It is given that sin x*cos 150 = 0 but 5 - cos x*sin 150 does not have any purpose.

sin x*cos 150 = 0 can be solved for x as cos 150 is not equal to 0, only sin x = 0. Also 0 < x < 360

sin x = 0

=> x = arc sin 0 = pi

The solution of the equation sin x*cos 150 = 0 is pi.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll shift the product -cos x*sin 150 to the left side:

sin x*cos 150 + cos x*sin 150 = 0.5

We'll recognize the formula:

sin(x+150) = 0.5

But sin(x+150) = cos (90 - x - 150) = cos (-x - 60)

sin(x+150) = - cos (x + 60)

We'll re-write the equation:

- cos (x + 60) = 1/2

x + 60 = arccos (-1/2)

x + 60 = 120

x = 60

or

x + 60 = 240

x = 240 - 60

x = 180

The solutions of the equation, located in the range (0,360) are: x = 60 degrees = pi/3 radians and x = 180 degrees = pi radians.

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