Question

How do you find the values of the other five trigonometric functions of the acute angle A with `sec A=7/3`?

Answer 1

For `hatA: opp= sqrt40, adj = 3 and hyp = 7`
Now you can write all six ratios.

Explanation:

Remember than the 6 basic trig functions only apply to right-angled triangles. Therefore, if you know the lengths of 2 sides you can use Pythagoras' Theorem to find the length of the third side.

Then you can easily write the ratios for all 6 functions.

In this case you have `sec A = 7/3 and sec theta = h/a`

The other side of this triangle is `sqrt(7^2- 3^2) = sqrt40`

For `hatA: opp= sqrt40, adj = 3 and hyp = 7`

Now we have:

`sin A = sqrt40/7" "cos A = 3/7" "tan A = sqrt40/3`

`cosec A = 7/sqrt40" "sec A = 7/3" "cot A = 3/sqrt40`