Checking and securing understanding of the unit circle

12 questions

1. A tangent to a curve at a given point is a line that intersects the curve at that point. Both the tangent and the curve have the same ___ at the given point.
2. What are the coordinates of P?
3. What are the coordinates of Q?
4. A right-angled triangle has a hypotenuse of 1 cm and a short side of 0.6 cm, what is the length of the third side of the triangle?
5. A right-angled triangle has a hypotenuse of 1 cm and a short side of 0.54 cm, what is the length of the third side of the triangle, to 2 decimal places?
6. A right-angled triangle has a hypotenuse of 2.6 cm and a short side of 1 cm, what is the length of the third side of the triangle?
7. What are the features of the unit circle?
8. The sine of an angle is the __________ of the point where the radius of the unit circle has been rotated through that angle.
9. The __________ of an angle is the x-coordinate of the point where the radius of the unit circle has been rotated through that angle.
10. The tangent of an angle is the __________ of the point where the line (the triangle’s hypotenuse) intersects the tangent line.
11. Match up the correct trigonometric values.
12. Using this diagram, what can be deduced?

License: OGL