# Find the exact value of all theta , domain is 0 degrees is less than or equal to theta is less than 360 degrees. for which cot theta = -1 over square root of 3.

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Expert Answers

hala718 | Certified Educator

`cot theta = -1/sqrt3`

But we know that `cot theta = (costheta)/(sintheta) `

`==gt (costheta)/(sintheta)= -1/sqrt3 `

`==gt -sin theta = sqrt3 costheta `

`==gt sin theta = -sqrt3 cos theta`

Also, we know that `sin^2 theta + cos^2 theta = 1`

`==gt (-sqrt3 costheta)^2 + cos^2 theta = 1 `

`==gt 3cos^2 theta + cos^2 theta = 1 `

`==gt 4cos^2 theta = 1 ==gt cos^2 theta = 1/4 `

`==gt cos theta = 1/2 `

`==gt sintheta = -sqrt3 cotheta = -sqrt3 (1/2) = sqrt3/2`

` ==gt tan theta = 1/(cot theta)= -sqrt3 ==gt sec theta = 1/(costheta)= 2 `

`==gt csctheta = 1/(sintheta)= 2/sqrt3 = (2sqrt3)/3)`