Respuesta :

Answer:

csc (theta) = 5/3

Step-by-step explanation:

If tan (theta) = 3/4

and tangent is the ratio of opposite/adjacent, OPP/ADJ, consider a triangle with theta and sides 3 and 4. The hypotenuse must be 5. You can calculate it or if you know, it is the pythagorean triple 3, 4, 5. See image.

Cosecant is the reciprocal of sine. Sin(theta) = 3/5

so csc(theta) = 5/3

Ver imagen lpina68
MrRoyal

The value of [tex]\csc(\theta)[/tex] is 5/3

What are trigonometry ratios?

Trigonometry ratios are used to determine the sides and angles in a right triangle

The trigonometry ratio is given as:

[tex]\tan(\theta) = \frac 34[/tex]

In a right triangle, if the tangent ratio is:

[tex]\tan(\theta) = \frac{x}{y}[/tex]

Then the cosecant ratio is:

[tex]\csc(\theta) = \frac{\sqrt{y^2 + x^2}}{x}[/tex]

By comparing:

[tex]\tan(\theta) = \frac 34[/tex] and [tex]\tan(\theta) = \frac{x}{y}[/tex]

We have:

x = 3 and y = 4

So, the above cosecant expression becomes

[tex]\csc(\theta) = \frac{\sqrt{4^2 + 3^2}}{3}[/tex]

Evaluate the exponents

[tex]\csc(\theta) = \frac{\sqrt{25}}{3}[/tex]

Evaluate the root

[tex]\csc(\theta) = \frac{5}{3}[/tex]

Hence, the value of [tex]\csc(\theta)[/tex] is 5/3

Read more about trigonometry ratios at:

https://brainly.com/question/10417664

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