Download MTH 112

MTH 112
Vocabulary Review:
Vertex of an angle
Initial side of an angle
Terminal side of an angle
Right angle
Straight angle
Acute angle
Obtuse angle
Supplement of an angle
Complement of an angle
Right triangle
Hypotenuse
Legs of a right triangle
Pythagorean Theorem
Sections 1.1 and 1.2
What is special about a 45o-45o-90o triangle?
What is special about a 30o-60o-90o 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 an example of the coordinates of a point
a.
on the y-axis
b.
in Quadrant II
c.
in Quadrant IV
d.
In Quadrant III
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 x-coordinates?
b.
In what two quadrants do all the points have negative y–coordinates?
6.
For points (x, y) in quadrant I, 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 is the ratio y/x
always negative?
8.
An angle in standard position has its vertex on the origin and its initial side on
the positive x-axis.
A positive angle goes in the counterclockwise direction from its initial side to its
terminal side.
Positve angle
A negative angle goes in the clockwise direction from its initial side to its terminal side.
In what quadrant would the terminal side of the angle in standard position lie?
a.
125o
c.
230o
b.
-15o
d.
-190o
e.
75o
9.
Label each of the terminal sides of an angle in standard position which are drawn
below. Assume they are all positive angles less than one full revolution.
Assume the angles with the x-axis are all 45°
Assume all the lines are at intervals of 30°.
Coterminal angles have the same terminal side when in standard position. For
example, 90° and -270° are coterminal angles. Angles may also be more than one
revolution. Thus 90° and 450° are also coterminal as are 90o and 90o – 2(360o) or
-630o.
10.
How many coterminal angles are there for 90°?
11.
i.
Sketch the angle and name a point on the terminal side of the angle (hint:
refer back to 45o-45o-90o and 30o-60o-90o triangles as needed.
ii.
Find the distance from the origin to that point.
iii.
Name another angle that is coterminal with the angle you have drawn.
a.
135°
b.
215°
c.
-30°
d.
-90°