To find cosec 60°, sec 60°, and cot 60°, we first need to understand the basic properties of these trigonometric functions.
1. cosec 60°: The cosecant function is the reciprocal of the sine function. Therefore, cosec 60° = 1/sin 60°.
Since sin 60° is √3/2, we have:
cosec 60° = 1/(√3/2) = 2/√3 = (2√3)/3.
2. sec 60°: The secant function is the reciprocal of the cosine function. Thus, sec 60° = 1/cos 60°.
We know that cos 60° is 1/2, so:
sec 60° = 1/(1/2) = 2.
3. cot 60°: The cotangent function is the reciprocal of the tangent function. Therefore, cot 60° = 1/tan 60°.
Since tan 60° is √3, we have:
cot 60° = 1/√3 = √3/3.
In summary:
- cosec 60° = (2√3)/3
- sec 60° = 2
- cot 60° = √3/3