Intro to Trigonometry

Front

What is the definition of the sine function in a right triangle?

Back

The sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse. It is represented as: \( \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \)

Front

What is the definition of the cosine function in a right triangle?

Back

The cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. It is represented as: \( \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \)

Front

What is the definition of the tangent function in a right triangle?

Back

The tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side. It is represented as: \( \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \)

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. It is represented as: \( a^2 + b^2 = c^2 \)

Front

If you know the lengths of the opposite and hypotenuse sides, which trig function do you use?

Back

You use the sine function.

Front

If you know the lengths of the adjacent and hypotenuse sides, which trig function do you use?

Back

You use the cosine function.

Front

If you know the lengths of the opposite and adjacent sides, which trig function do you use?

Back

You use the tangent function.

Front

What is the relationship between sine, cosine, and tangent?

Back

The tangent function can be expressed in terms of sine and cosine: \( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \)

Front

What is the value of \( \sin(30^\circ) \)?

Back

The value of \( \sin(30^\circ) \) is \( \frac{1}{2} \).

Front

What is the value of \( \cos(60^\circ) \)?

Back

The value of \( \cos(60^\circ) \) is \( \frac{1}{2} \).