MATH SOLVE

5 months ago

Q:
# Consider △DFE. What are the inputs or outputs of the following trigonometric ratios? Express the ratios in simplest terms.sin(?) = 4/5cos(F) = ?tan(D) = ?

Accepted Solution

A:

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 Pythagoren theorem to get the other side as follows:

hypotenuse^2 = side1^2 + side2^2

5^2 = 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 :)

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 Pythagoren theorem to get the other side as follows:

hypotenuse^2 = side1^2 + side2^2

5^2 = 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 :)