Question

Write each trig ratio as a fraction. Write in simplest form. A 10 6 C B 8. Sin A = Sin C = Cos A= Cos C = Tan A = Tan C =

Answer 1

we are asked to determine the ratio of different trigonometric functions of a right triangle. To do that let's remember the definition of an adjacent and opposite side.

The adjacent side is the side that touches the angle we are using for the trigonometric function, the opposite side is the side that is in front of the angle.

Now let's define each trigonometric function:

`\begin{gathered} \sin x=(opposite)/(hypotenuse) \\ \cos x=(adajacent)/(hypotenuse) \\ \tan x=(opposite)/(adjacent) \end{gathered}`

Using the definition we can find the values of the ratios for each function.

For angle A we have the sine function:

`\sin A=(8)/(10)=(4)/(5)`

The cosine function:

`\cos A=(6)/(10)=(3)/(5)`

The tangent function:

`\tan A=(8)/(6)=(4)/(3)`

For angle C we have the sine function:

`\sin C=(6)/(10)=(3)/(5)`

The cosine function:

`\cos C=(8)/(10)=(4)/(5)`

the tangent function:

`\tan C=(6)/(8)=(3)/(4)`