3.1-3.3graphing trig equations

Front

What is the sine function?

Back

The sine function, denoted as \( \sin(\theta) \), is a trigonometric function that relates the angle \( \theta \) to the ratio of the length of the opposite side to the hypotenuse in a right triangle.

Front

What is the cosine function?

Back

The cosine function, denoted as \( \cos(\theta) \), is a trigonometric function that relates the angle \( \theta \) to the ratio of the length of the adjacent side to the hypotenuse in a right triangle.

Front

What is the tangent function?

Back

The tangent function, denoted as \( \tan(\theta) \), is a trigonometric function that relates the angle \( \theta \) to the ratio of the length of the opposite side to the adjacent side in a right triangle.

Front

What is the cotangent function?

Back

The cotangent function, denoted as \( \cot(\theta) \), is the reciprocal of the tangent function, defined as \( \cot(\theta) = \frac{1}{\tan(\theta)} = \frac{\cos(\theta)}{\sin(\theta)} \).

Front

What is the secant function?

Back

The secant function, denoted as \( \sec(\theta) \), is the reciprocal of the cosine function, defined as \( \sec(\theta) = \frac{1}{\cos(\theta)} \).

Front

What is the cosecant function?

Back

The cosecant function, denoted as \( \csc(\theta) \), is the reciprocal of the sine function, defined as \( \csc(\theta) = \frac{1}{\sin(\theta)} \).

Front

What is the period of the sine function?

Back

The period of the sine function is \( 2\pi \), meaning it repeats every \( 2\pi \) radians.

Front

What is the period of the cosine function?

Back

The period of the cosine function is \( 2\pi \), meaning it repeats every \( 2\pi \) radians.

Front

What is the period of the tangent function?

Back

The period of the tangent function is \( \pi \), meaning it repeats every \( \pi \) radians.

Front

How does the graph of \( \sin(2\theta) \) differ from \( \sin(\theta) \)?

Back

The graph of \( \sin(2\theta) \) has a period of \( \pi \) instead of \( 2\pi \), resulting in it oscillating twice as fast.