Trigonometric functions
Connect periods, graphs, and sine/cosine amplitudes with rotation and repeated change.
Meaning
Defining cosine and sine using unit-circle coordinates extends them beyond acute angles. Sine and cosine repeat between -1 and 1; tangent is undefined where cosine is zero. One full turn returns to the same unit-circle point, so sine and cosine repeat every 2π. Multiplying sine by 2 doubles the vertical coordinate to a range from −2 to 2. Tangent is sin x/cos x, so it is undefined when the denominator is zero.
Example
Practice for this concept
Scope and references
Topics
Sine, cosine, tangent, periods, amplitudes, graphs
Learning goal
Connect periods, graphs, and sine/cosine amplitudes with rotation and repeated change.
Helpful background
Connect unit-circle angles with function inputs and outputs.
Trigonometric functions
These ordinary choice questions provide limited practice in this concept. They do not establish independent solution, full-concept performance, or mastery.