F-TF. Trigonometric Functions

F-TF.A. Extend the domain of trigonometric functions using the unit circle.

• Exploring Sinusoidal Functions

F-TF.A.1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

• Bicycle Wheel
• What exactly is a radian?

F-TF.A.2. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

• Properties of Trigonometric Functions
• Trig Functions and the Unit Circle
• Trigonometric functions for arbitrary angles (radians)
• Trigonometric Identities and Rigid Motions

F-TF.A.3. Use special triangles to determine geometrically the values of sine, cosine, tangent for $\pi/3$, $\pi/4$ and $\pi/6$, and use the unit circle to express the values of sine, cosines, and tangent for $\pi - x$, $\pi + x$, and $2\pi - x$ in terms of their values for $x$, where $x$ is any real number.

• Equilateral triangles and trigonometric functions
• Special Triangles 1
• Special Triangles 2

F-TF.A.4. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

• Properties of Trigonometric Functions

F-TF.B. Model periodic phenomena with trigonometric functions.

F-TF.B.5. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

• As the Wheel Turns
• Foxes and Rabbits 2
• Foxes and Rabbits 3
• Hours of Daylight 1

F-TF.B.6. Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

• No tasks yet illustrate this standard.

F-TF.B.7. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

• No tasks yet illustrate this standard.

F-TF.C. Prove and apply trigonometric identities.

• Coordinates of Points on a Circle

F-TF.C.8. Prove the Pythagorean identity $\sin^2(\theta) + \cos^2(\theta) = 1$ and use it to find $\sin(\theta)$, $\cos(\theta)$, or $\tan(\theta)$ given $\sin(\theta)$, $\cos(\theta)$, or $\tan(\theta)$ and the quadrant of the angle.

• Calculations with sine and cosine
• Finding Trig Values
• Trigonometric Ratios and the Pythagorean Theorem

F-TF.C.9. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

• Coordinates of equilateral triangles
• Sum and Difference angle formulas