mathQuadrant IIcot  =  -3 sin  =?

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given that cot (x) = -3

We need to find sin(x).

We know that:

cot(x) = cos(x)/ sin(x) = -3

==> cos(x) = -3*sin(x) ...............(1)

Also, we know that:

sin^2 x + cos^2 x = 1

==> sin^2 x + (-3sinx)^2 = 1

==> sin^2 x + 9sin^2 x = 1

==> 10sin^2 x = 1

==> sin^2 x = 1/10

==> sin(x) = sqrt(1/10) = 1/sqrt10

==> sin(x) = 1/sqrt(10) = sqrt10 / 10

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

In the second quadrant, the sine function is also positive.

cot t= cos t/sin t

cos t/sin t = -3

cos t = -3sin t

We'll apply the fundamental formula of trigonometry:

(sin t)^2 + (cos t)^2 = 1

(sin t)^2 + (-3sin t)^2 = 1

(sin t)^2 + 9(sin t)^2 = 1

10(sin t)^2 = 1

(sin t)^2 = 1/10

sin t = 1/sqrt10

sin t = sqrt10/10

Note: We'll keep only the positive value for sin t.

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