Question

If `sin θ = 1/sqrt(11)`, then cot θ equals

Options

• `sqrt(11)/sqrt(10)`

• `sqrt(10)/sqrt(11)`

• `sqrt(10)`

• `sqrt(11)`

Answer 1

`bb(sqrt(10))`

Explanation:

1. Identify the given value

The sine of an angle θ is defined in a right triangle as the ratio of the perpendicular (p) to the hypotenuse (h).

`sin θ = p/h`

= `1/sqrt(11)`

From this, we can let:

p = 1

`h = sqrt(11)`

2. Find the adjacent side (base)

Using the Pythagorean theorem (h² = p² + b²), where b is the base:

`(sqrt(11))^2 = 1^2 + b^2`

11 = 1 + b²

b² = 10

`b = sqrt(10)`

3. Calculate cotangent

The cotangent of an angle is the ratio of the base (b) to the perpendicular (p).

`cot θ = b/p`

`cot θ = sqrt(10)/1`

= `sqrt(10)`

Depending on which quadrant θ lies in, the value can be positive or negative. Since no quadrant is specified, the general solution is `± sqrt(10)`.