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Consider △DFE. What are the inputs or outputs of the following trigonometric ratios? Express the ratios in simplest terms.

Respuesta :

Louli
Answer:
sin F = 4/5
cos F = 3/5
tan D = 3/4

Explanation:
First, we have sin an angle = 4/5
In a right-angled triangle:
sin theta = opposite / hypotenuse
This means that in triangle DFE:
The hypotenuse = 5 units
one of the sides = 4 units
Use Pythagorean theorem to get the other side as follows:
hypotenuse^2 = side1^2 + side2^
25^2 = 4^2 + side2^2
side2^2 = 9
The second side of the triangle = 3 units

The special trig functions are as follows:
sin theta = opposite / hypotenuse
cos theta = adjacent / hypotenuse
tan theta = opposite / adjacent
From the attached figure and based on the calculations above:
sin F = 4/5
cos F = 3/5
tan D = 3/4
Hope this helps :)

Ver imagen Louli
snehashish65

The inputs of the given triangle are the length of sides that are 5 units, 4 units and 3 units, for which the trigonometric ratios are 3/4 , 5,4 and 3/5 respectively.

Let us consider a triangle, such that:

Base = DE = 5 units

Hypotaneous = EF = 4 units

Height/perpendicular = DF = 3 units

Now, apply the trigonometric functions in the above triangles to obtain the outputs as,

We know  that sine function is,

[tex]sine = \dfrac{Perpendicular}{hypotanous} \\\\sine = \dfrac{3}{4} \;\rm units[/tex]

And cosine function is,

[tex]cosine = \dfrac{base}{hypotanous} \\\\cosine = \dfrac{DE}{EF} \\\\cosine = \dfrac{5}{4}\;\rm units[/tex]

And tangent function is,

[tex]tan = \dfrac{perpendicular}{base} \\\\tan = \dfrac{DF}{DE} \\\\tan = \dfrac{3}{5}\;\rm units[/tex]

Thus, we can conclude that the inputs of the given triangle are the length of sides that are 5 units, 4 units and 3 units, for which the trigonometric ratios are 3/4 , 5,4 and 3/5 respectively.

Learn more about the trigonometric ratios here:

https://brainly.com/question/25122832

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