Question

If cot theta= 2/3, what is the value of ccs theta

Answer 1

1. csc Θ = √13/3

Explanation:

cot Θ=1 / tan Θ = cos Θ/sin Θ

csc Θ=1 /sin Θ

cot Θ = 2/3 = cos Θ/sin Θ

cos Θ = adj side / hypotenuse; sin Θ = opp side / hypotenuse so cot Θ = adj side / opp side

In the picture below using Pythagoras theorem a² + b² = c² you can find c as √2² + 3² = √13

sin Θ = 3/ √13

so csc Θ = 1/sin Θ = √13/3

Answer 2

A. √13/3

Explanation:

Let's draw this in the coordinate plane. See attachment.

Cotangent is adjacent / opposite, and we see that if we drop a perpendicular down, we get a right triangle with leg lengths of 2 and 3. Use the Pythagorean Theorem to find the hypotenuse:

c = √(2² + 3²) = √(4 + 9) = √13

Cosecant is hypotenuse / opposite, so since the opposite is 3 and the hypotenuse is √13, then csc(θ) = √13/3.

The answer is thus A.