Drag the point [math]P[/math] and activate the checkboxes to explore how the sine and cosine of an angle [math]\alpha[/math] change sign and value on the unit circle, then answer the questions below the app.
What are the signs of [math]\sin\frac{\pi}{12}[/math] and [math]\cos\frac{\pi}{12}[/math] ?
In which quadrant does [math]\alpha=-\frac{2}{3}\pi[/math] lie?[br]What are the signs of its sine and cosine?
An angle [math]2x[/math] lies in the third quadrant.[br]What is the sign of [math]\cos\left(x\right)[/math]?
How many angles (if any) have a sine equal to [math]\frac{1}{3}[/math]?[br]If they exist, what can you say about their positions in the unit circle?
How many angles (if any) have a cosine equal to [math]-\frac{2}{3}[/math]?[br]If they exist, what can you say about their positions in the unit circle?
How many angles (if any) have a sine equal to [math]\frac{5}{3}[/math]?[br]If they exist, what can you say about their positions in the unit circle?