Question

Solve the equation sin sq x = 3cos sq x.

The value of x that satisfies the equation if x lies in the second quadrant is °.

The value of x that satisfies the equation if x lies in the third quadrant is

Answer 1

The value of x that satisfies the equation if x lies in the second quadrant is 120

The value of x that satisfies the equation if x lies in the third quadrant is

240

Explanation:

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Answer 2

Second quadrant = 120°.

Third quadrant = 210°

Explanation:

We are given that:

`sin^2(x) = 3cos^2(x)`

The following property is known:

`sin^2(x) +cos^2(x)=1\\`

Combining both expressions:

`sin^2(x) =1-cos^2(x)\\sin^2(x) = 3cos^2(x)\\\\1-cos^2(x) = 3cos^2(x)\\cos^2(x)=(1)/(4)\\cos(x)=\pm (1)/(2)`

If x lies in the second quadrant, then cos(x) = -1/2:

`x=cos^(-1)(1/2)\\x=120^o`

The value of x that satisfies the equation if x lies in the second quadrant is 120°.

If x lies in the third quadrant, then cos(x) = -1/2:

`x=120+90=210^o`

The value of x that satisfies the equation if x lies in the third quadrant is 210°