Alg2.6 Trigonometric Functions
- I can use the Pythagorean Theorem to find coordinates of points on a circle centered at the origin.
- I understand that a periodic function is one with outputs that repeat at regular intervals.
- I understand how to use trigonometry to express the coordinates of a point in quadrant 1 that is 1 unit away from the origin.
- I understand that a radian angle measurement is the ratio of the arc length to the radius of the circle.
- I understand that points on a unit circle can be defined by their coordinates or by an angle of rotation.
- I can find different angles on the unit circle and estimate their coordinates.
- I can use the Pythagorean Identity to calculate values of coordinates given one coordinate to start from.
- I understand that the coordinates of a point on the unit circle at $\theta$ radians can be written as $(\cos(\theta),\sin(\theta))$.
- I can use the Pythagorean Identity to find the values of cosine, sine, and tangent of an angle if I know one of them and the quadrant of the angle.
- I can use cosine and sine to figure out information about points rotating in circles.
- I understand that the graph of a periodic function can look like a wave whose outputs repeat between the same maximum and minimum values.
- I can use the coordinates of points on the unit circle to graph the cosine and sine functions.
- I understand how to find the values of cosine and sine for inputs greater than $2\pi$ radians.
- I understand how to find the values of cosine and sine for inputs less than 0 radians.
- I can explain why the tangent function has a period of $\pi$.
- I understand why the graph of tangent has asymptotes.
- I can write a trigonometric function to represent situations with different amplitudes and midlines.
- I can graph a horizontal translation of a trigonometric function.
- I can use the amplitude and midline of a trigonometric equation to describe a situation.
- I can identify the midline, amplitude, and horizontal translation of a trigonometric function given a graph or equation.
- I can find the period of a trigonometric function using an equation or graph.
- I can ask questions to figure out how a trigonometric function was transformed.
- I can create an equation of a trigonometric function using information about its graph.
- I can represent a circular motion situation using a graph and an equation.
- I can create a model of data that is approximately periodic and use the model to make predictions.