Which equation is correct? (4 points)

Question

cos x° = adjacent ÷ opposite

tan x° = opposite ÷ adjacent

cos x° = opposite ÷ adjacent

tan x° = adjacent ÷ opposite

Answer 1

Let's clarify the definitions of the trigonometric functions for a right triangle:

1. Sine (sin): \( \sin x° = \frac{\text{opposite}}{\text{hypotenuse}} \)
2. Cosine (cos): \( \cos x° = \frac{\text{adjacent}}{\text{hypotenuse}} \)
3. Tangent (tan): \( \tan x° = \frac{\text{opposite}}{\text{adjacent}} \)

Given these definitions, let's analyze the equations provided:

1. cos x° = adjacent ÷ opposite - Incorrect (It should be adjacent divided by hypotenuse).
2. tan x° = opposite ÷ adjacent - Correct.
3. cos x° = opposite ÷ adjacent - Incorrect (It should be adjacent divided by hypotenuse).
4. tan x° = adjacent ÷ opposite - Incorrect (It should be opposite divided by adjacent).

So, the correct equation among the options provided is:

tan x° = opposite ÷ adjacent.