Trigonometric Ratios

Front

What is the definition of cosine in a right triangle?

Back

Cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse: \( \cos(X) = \frac{adjacent}{hypotenuse} \).

Front

What is the value of \( \cos(X) \) if it is given as \( \frac{15}{17} \)?

Back

The value of \( \cos(X) \) is \( \frac{15}{17} \).

Front

How do you find \( \sin(X) \) if you know \( \cos(X) \)?

Back

You can use the Pythagorean identity: \( \sin^2(X) + \cos^2(X) = 1 \). If \( \cos(X) = \frac{15}{17} \), then \( \sin(X) = \sqrt{1 - \left(\frac{15}{17}\right)^2} = \frac{8}{17} \).

Front

What is the definition of sine in a right triangle?

Back

Sine is defined as the ratio of the length of the opposite side to the length of the hypotenuse: \( \sin(X) = \frac{opposite}{hypotenuse} \).

Front

What is the value of \( \sin(X) \) if it is given as \( \frac{20}{29} \)?

Back

The value of \( \sin(X) \) is \( \frac{20}{29} \).

Front

What is the relationship between sine and cosine in a right triangle?

Back

Sine and cosine are related through the Pythagorean identity: \( \sin^2(X) + \cos^2(X) = 1 \).

Front

How do you calculate \( \sin(X) \) if \( \sin(X) = \frac{27}{45} \)?

Back

You can simplify \( \sin(X) \) to \( \frac{3}{5} \) by dividing both the numerator and denominator by 9.

Front

What is the definition of tangent in a right triangle?

Back

Tangent is defined as the ratio of the length of the opposite side to the length of the adjacent side: \( \tan(X) = \frac{opposite}{adjacent} \).

Front

If \( \cos(D) = \frac{6}{10} \), what is the simplified value?

Back

The simplified value of \( \cos(D) \) is \( \frac{3}{5} \).

Front

What is the value of \( \tan(X) \) if \( \sin(X) = \frac{3}{5} \) and \( \cos(X) = \frac{4}{5} \)?

Back

The value of \( \tan(X) \) is \( \frac{\sin(X)}{\cos(X)} = \frac{3/5}{4/5} = \frac{3}{4} \).