The 6 Trig Ratios

For any right triangle, there are six trig ratios: Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).

Here are the formulas for these six trig ratios:

$The 6 trig ratios img 1$

$The 6 trig ratios img 2$

$The 6 trig ratios img 3$

Given a triangle, you should be able to identify all 6 ratios for all the angles (except the right angle).

Let's start by finding all 6 ratios for angle A.

$The 6 trig ratios img 7$

$The 6 trig ratios img 4$

$The 6 trig ratios img 5$

$The 6 trig ratios img 6$

Notice that the csc, sec, and cot can be found simply by flipping the ratio they are associated with. Or,
you can use the formulas.

To find the 6 ratios for angle B, just start over again and rethink them looking at angle B instead of angle A. This means that the opposite and the adjacent sides switch while the hypotenuse stays the same. Here are the 6 ratios for angle B:

$The 6 trig ratios img 8$

$The 6 trig ratios img 9$

$The 6 trig ratios img 10$

Go back and compare the ratios from angle A with the ratios from angle B. You will notice quite a few relationships.

Practice: Find the following:

$The 6 trig ratios img 11$ 1. Sin A
2. Cos A
3. Tan A
4. Csc A
5. Sec A
6. Cot A
7. Sin B
8. Cos B
9. Tan B
10. Csc B
11. Sec B
12. Cot B

Answers: $The 6 trig ratios img 12$

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The 6 Trig Ratios

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