Question

Urgent, please i will give brainliest

Answer 1

Answer:

1). First option √13/3

2).  Third option 3.2362

3). Third option   60/11

Step-by-step explanation:

1). To find cosec θ

It is given cot θ = 2/3

We have cotθ = adjacent side /Opposite side

Hypotenuse = √(adjacent  side² + opposite side²) =√(2² + 3²) = √13

Cosec θ = Hypotenuse/opposite side = √13/3

2). To find cosec θ

It is given that,

Sinθ  = 0.3090

Cosec θ = 1/Sinθ  = 1/0.3090 = 3.2362

3). To find cot θ

It is given that,

Tanθ  = 11/60

Cot θ  = 1/tan θ  = 1/(11/60) = 60/11

Answer 2

Answer:

1. $\frac{\sqrt{13} }{3}$

2. 3.2362

3. $\frac{60}{11}$

Step-by-step explanation:

1.

Cot is the trigonometric ratio defined by "adjacent" over "opposite". So, adjacent = 2 and opposite = 3.

By pythagorean theorem, we have the "hypotenuse" as  $\sqrt{2^2+3^2}=\sqrt{13}$

Csc is defined as the trig ratio "hypotenuse" over "opposite". We know the sides, so Csc $\theta$ = $\frac{\sqrt{13} }{3}$

First answer choice is right.

2.

By definition, Csc $\theta$ is the inverse of Sine $\theta$. If given the value of sin theta, to find value of csc theta, we take the reciprocal of it. Hence:

$Csc\theta=\frac{1}{0.3090}\\=3.2362$

Third answer choice is right.

3.

By definition tan and cot are inverse of each other. So the value of tan is the reciprocal of the value of cot. We can simply "flip" the value of tan theta to get the value of cot theta. Hence:

$Cot\theta=\frac{60}{11}$

Third answer is right.