# Determine the exact values of the trigonometric functions of the acute angle A, given tan A =3/7 ?

##### 2 Answers

see explanation

#### Explanation:

Tan A = 3/7 specifies a right triangle with base = 7, height = 3.

(because by definition Tan A = height/base).

The hypotenuse of the triangle is then

And with this information, you can calculate the other trig values for the triangle:

...and, as a final sanity check, you can use the alternate definition for Tan A:

...which checks out.

I won't calculate sec a, csc a, cot a for you, you should be able to take it from here, since:

GOOD LUCK

#### Explanation:

Given:

Use the identity

Use the identity

Using the identity

Using the identity

Use the identity