Question

Find the exact value of the indicated trigonometric functions for the acute angle α : Given cot α = 3 and 3/7 , find cos α and tan α .

(a) cos α = 3/√58, tan α = √58/3
(b) cos α = √58/3, tan α = 3/√58
(c) cos α = 3/7, tan α = 7/3
(d) cos α = 7/3, tan α = 3/7

Answer 1

For the given values of cot(α), we can find tan(α) = 7/24 and cos(α) = 3/√58.

Step-by-step explanation:

We are given that cot(α) = 3 and 3/7.

Since cot(α) = 1/tan(α), we can say that tan(α) = 1/cot(α).

Therefore, tan(α) = 1/(3 and 3/7).

To find the exact value of tan(α), we can convert the mixed number 3 and 3/7 to an improper fraction: 3 and 3/7 = (7*3 + 3)/7 = 24/7.

So, tan(α) = 1/(24/7) = 7/24.

Now, to find cos(α), we can use the identity cos²(α) + sin²(α) = 1.

We know that cot(α) = cos(α)/sin(α), so cos(α) = cot(α) * sin(α).

Substituting the given values, cos(α) = (3 and 3/7) * sin(α).

Since sin(α) = 1/csc(α), we can find cos(α) = (3 and 3/7) * (1/csc(α)).

Therefore, cos(α) = (3 and 3/7) * (1/(√(1 + cot²(α)))) = (3 and 3/7) * (1/(√(1 + (24/7)²))).

Simplifying the expression, cos(α) = 3/√58.