Given the function value of the acute​ angle, find the other five trigonometric function values.

Question

cos √7/7

Answer 1

Hello Natalee,

I have included a drawing of a right triangle. By definition, cosine is adjacent over hypotenuse so using angle A as reference, cos A = adjacent / hypotenuse = √7 / 7

You'd need to use Pythagorean theorem to find the missing side a (drawn in blue):

a² + b² = c² ---> a² + 7 = 49 --> a² = 42 ---> a = √42

You now have everything you need to find the other 5 trig functions:

1. sin A = opposite/hypotenuse = √42 / 7
2. tan A = opposite/adjacent = √42 / √7 = (√7 * √6) / √6 = √6
3. cot A = adjacent/opposite = √7 / √42 = √7 / (√7 * √6) = 1/√6 = √6 / 6
4. sec A = hypotenuse/adjacent = 7/√7 = √7
5. csc A = hypotenuse/opposite = 7/√42 = 7√42 / 42 = √42 / 6