Question

Evaluate the 6 trigonometric functions of angle A

Answer 1

Let's first define the 6 trigonometric functions for a better understanding (here, O is "opposite," A is "adjacent," and H is "hypotenuse"):

`sin(x) = (O)/(H)`

`cos(x) = (A)/(H)`

`tan(x) = (O)/(A)`

`csc(x) = (H)/(O)`

`sin(x) = (H)/(A)`

`sin(x) = (A)/(O)`

Now, all we need to do is identify the opposite, and adjacent to the angle and solve for the hypotenuse based on given information. Let's first solve for hypotenuse:

`c^2 = a^2 + b^2`

`c = √(a^2+b^2)`

`c = √(7^2+4^2) = √(65)`

We have all the information we need:

`H = √(65)`

`O = 7`

`A = 4`


We can now solve for each ratio:

`sin(x) = (7)/( √(65) ) = (7 √(65) )/(65)`

`cos(x) = (4)/( √(65) ) = (4 √(65) )/(65)`

`tan(x) = (7)/( 4 )`

`csc(x) = ( √(65) )/(7)`

`sec(x) = ( √(65) )/(4)`

`cot(x) = (4)/(7)`

Hope this helped!