Thermal Energy
1.
The relative masses of oxygen and hydrogen molecules are 32 and 2 respectively. For any given
temperature, the ratio
root mean square speed of oxygen molecules
is given by
root mean square speed of hydrogen molecules
A
1
16
B
1
4
C
4
D
1
9.1 Polar Coordinates
Recording the position of an object using the
distance from a fixed point and an angle made
with a fixed ray from that point uses a polar
coordinate system.
The polar axis is usually a horizontal ray
directed towards the right from t
5.8 Law of Cosines
The Law of Cosines
a2 = b2 + c2 - 2bc cos A
b2 = a2 + c2 - 2ac cos B
c2 = a2 + b2 - 2ab cos C
SAS
SSS
(SSS or SAS)
AREA of a triangle given the measure of all three
sides (SSS)
HW pg. 331 #11 15 odd, 19 21odd, 27, 33, 35
5-3 Trig Functions and the Unit Circle
The unit circle is a circle of radius 1.
Sign rules for coordinates
Use the unit circle to find each value.
Find the value of the trig function
Ex 1) sin 150o
Ex) cos 210o
HW pg. 296 #15-29 odd, 31-35 all, 38-44 even
5.6 Law of Sines
To solve triangles that are not right triangles if given
2 angles and one side, use the
AREA OF A TRIANGLE GIVEN TWO SIDES AND THEIR
INCLUDED ANGLE (SAS)
AREA OF A TRIANGLE GIVEN ONE SIDE AND TWO ANGLES
(AAS)
HW 5.6 .pg. 316 #11-15 odd, 1
5-5 Solving Right Triangles
Sometimes you know the trigonometric values of an angle but not the
measure of the angle. In this case you need to use an inverse of the
trigonometric function to find the degree measure of the angle.
The Trigonometric function
5-4 Applying Trig Functions
Solve each problem. Round to the nearest tenth.
Ex 1) If b = 13 and m A = 76o, find a
Ex 2) If m P = 35o and r = 14, find q
P
R
Q
Ex 3) If a rope connected to the top of a tent makes a 52 o15' with
the level ground, how long th
5.2 Trigonometric Ratios
In a right triangle, one angle measures 90o
The two remaining angles (acute angles) A & B are
complementary
m
A+m
B = 90o
The longest side c is called the hypotenuse.
The other two sides a and b are called legs.
c
a
b
An important
Chapter 8 Vectors
x2 x 1 , y 2 y 1
Ordered Pair - P1P2 is
|P1 P2|= ( x 2x 1) 2+ ( y 2 y 1 )2
Magnitude of a Vector
Horizontal and vertical components
x = v cos
y = v sin
Chapter 9 Polar Coordinates
Distance Formula in Polar Plane given
Polar Coordinat
ADVANCED MATH FINAL EXAM
Stevenson
TUESDAY, MAY 3, 2016 - 8:30 9:45 COUGAR DOME
Textbook due by 8:30am Tuesday, May 3
You must return the textbook that was issued to you at the beginning of the year
If you lost your textbook, you must pay a $70 replacemen
5.1 Angles and Degree Measures
Angle - rotation of two rays that share a fixed endpoint
Initial side - fixed ray of the angle (where the angle starts)
Terminal side - second ray rotates to form this angle (where the angle stops)
Vertex - fixed endpoint (w
2.1 Systems of Equations
A SYSTEM OF EQUATIONS is a set of two or more equations. To "solve" a system of
equations means to find values for the variables in the equation, which make all the
equations true at the same time.
The characteristics of the types