Question

If sine theta almost-equals 0. 3090 , what is the approximate value of csc Theta? 0. 5559 1. 3090 3. 2362 10. 4733.

Answer 1

Reciprocal of trigonometric ratios are also trigonometric ratios. The approximate value of csc(θ) for the corresponding given value of sin(θ) is given by: Option: C: 3.2362

What are the six trigonometric ratios?

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

$\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}$

Thus, we see that $\sin(\theta) = \dfrac{1}{\csc{\theta}}$ for a specific angle θ, we get:

Actually, reciprocal of each trigonometric ratio will be a trigonometric ratio, for specific angle.

For the considered case, we're given that,

$\sin(\theta) \approx 0.3090$

$\sin(\theta) = \dfrac{1}{\csc(\theta)}\\\\\csc(\theta) = \dfrac{1}{\sin(\theta)} \approx\dfrac{1}{0.3090} \approx 3.2362$

Thus, the approximate value of csc(θ) for the corresponding given value of sin(θ) is given by: Option: C: 3.2362

Learn more about trigonometric ratios here:

brainly.com/question/22599614

Answer 2

The value of csc(θ) is 3.2362.

We have given that

sin(θ)=0. 3090

Now we have to find that what is the value of csc(θ)

What is the relation between cos(θ)and sin(θ)

csc(θ)=1/sin(θ)........(1)

Therefore by using (1)

csc(θ)=1/0. 3090........   use the value of sin(θ)

So simplify above we get,

csc(θ)=3.2362

Therefore we get

The value of csc(θ) is 3.2362.

To learn more about the trigonometric identities visit:

brainly.com/question/22591162