Question

What angle in degrees corresponds to a cotangent of √3?

a) 30 degrees
b) 45 degrees
c) 60 degrees
d) 90 degrees

Answer 1

`\Large \textsf{Read below}`

Step-by-step explanation:

`\Large \text{$ \sf tan\:\Theta = (sin\:\Theta)/(cos\:\Theta)$}`

`\Large \text{$ \sf cot\:\Theta = (1)/(tan\:\Theta)$}`

`\Large \text{$ \sf cot\:\Theta = (cos\:\Theta)/(sin\:\Theta)$}`

`\Large \text{$ \sf √(3) = (cos\:\Theta)/(sin\:\Theta)$}`

`\Large \text{$ \sf cos\:\Theta = √(3)\:.\:sin\:\Theta$}`

`\Large \boxed{\text{$ \sf sin^2\:\Theta + cos^2\:\Theta = 1$}}`

`\Large \text{$ \sf sin^2\:\Theta + [\:√(3)\:.\:sin\:\Theta\:]^2 = 1$}`

`\Large \text{$ \sf sin^2\:\Theta + 3\:sin^2\:\Theta = 1$}`

`\Large \text{$ \sf 4\:sin^2\:\Theta = 1$}`

`\Large \text{$ \sf sin^2\:\Theta = (1)/(4)$}`

`\Large \text{$ \sf sin\:\Theta = (1)/(2)$}`

`\Large \boxed{\boxed{\text{$ \sf \Theta = 30^(\circ)$}}}`

Answer 2

The angle that corresponds to a cotangent of √3 is 30 degrees, as it is the reciprocal of the tangent of 30 degrees.The angle in degrees that corresponds to a cotangent of √3 is 30 degrees.

Step-by-step explanation:

The angle in degrees that corresponds to a cotangent of √3 is 30 degrees. To find this, recall that the cotangent function is the reciprocal of the tangent function. Therefore, if cot(θ) = √3, then tan(θ) = 1/√3. Looking at the standard angles in trigonometry, we recognize that tan(30°) = 1/√3. Hence, θ = 30° is the angle we are searching for.