Download 1.1 VOCABULARY REVIEW vertex of an angle initial side of an

1.1 VOCABULARY REVIEW
vertex of an angle
right triangle
initial side of an angle
hypotenuse
terminal side of an angle
legs
right angle
Pythagorean Theorem
straight angle
obtuse angle
acute angle
supplement of an angle
complement of an angle
What is special about a 45o­45o­90o triangle?
What is special about a 30o­60o­90o triangle?
On the graph place labels for each of the items in the appropriate places.
Quadrant I, Quadrant II, Quadrant III, Quadrant IV, origin
1. Give examples for coordinates of a point
a. On the y­axis
b. In quadrant 2
c. In quadrant 4
d. In quadrant 3
2. What is the general equation for a circle of radius r centered at the origin? Give the general equation, an equation of a specific circle, and sketch it.
3. What is the distance formula to find the distance between two points and how is it related to the Pythagorean theorem?
4. Find the distance between (3, 5) and (­3, 3)
and illustrate it on a graph.
5.
a.
In what two quadrants do all the points have negative x­coordinates?
b.
In what two quadrants do all the points have negative y­coordinates?
6. For points (x, y) in quadrant 1, the ratio y/x is always positive because x and y are always positive. In what other quadrants is the ratio y/x always positive?
7.
For points (x, y) in quadrant II, the ratio y/x is always negative because x is negative and y is positive in quadrant II. In what other quadrant(s) is the ratio y/x always negative?
An angle in standard position has its vertex on the origin and its initial side on the positive x­axis.
A positive angle goes in counterclockwise direction from its initial side to its terminal side.
A negative angle goes in clockwise direction from its initial side to its terminal side.
8.
Label each of the terminal sides of an angle in standard position which is drawn below.
Assume these are at 30o intervals.
Coterminal angles have the same terminal side when in standard position. o
For example, 90o and ­270 are coterminal angles. Angles may also be more than one revolution. Thus 90o and 450o are coterminal.
9.
10.
How many coterminal angles are there for 90°?
i.
ii.
iii.
Name a point on the terminal side of the angle.
Find the distance from the origin to that point.
Name another angle that is coterminal with the angle you have drawn.
a.
135°
b.
225°
c.
­45°
d.
­90°