Download 1. cos x)(cot x) 1 in x)(1 ( = ( − s + 1 ) 2. + = csc θ 2

Sam Humphreys and Cody Krutzsch
Semester 2 Final Project!
Chapter 5: Trig
Solve each trigonometric identity.
1. (cos x)(cot x) = (1 − sin x)(1 +
2.
sin θ
1−cos θ
+
sin θ
1+cos θ
= 2 csc θ
Chapter 6: Systems
1.
A=
B=
Find A • B
Find the inverse using augmented matrices.
2.
1
sin x
)
Chapter 7: Conics
1. Cody and Sam are trying to figure out this crazy unit that Mr. Kohmetscher is teaching
them. They came into school early one day and saw a note left by him. ​Graph this and
and label XXX points and you get 100% for this semester’s grade​. Can you graph it and
get 100%?
x2 + 10x + y 2 + 18x =− 6
2. John was a professor at Samford University. His boss says he must graph this equation to keep
his job, but John was not sure if he could do it. He was given limited information.
Focus: (7, −5
)
2
Directrix; y = −13
2
Graph the equation
Chapter 7: Parametrics
1. Sketch each curve, indicating the starting and stopping point as well as direction.
Use − 1 ≤ t ≤ 5, △t = 1
a. x = 1 − √t and y = t + 1
b. x = 13 − 2 and y = |t − 2|
2. Jeff Wilkins punts a football at an angle of 52 ° up from the ground. He punts the football at
a speed of 22 meters per second. The football is kicked at a height of 1.3 meters above the
ground.
a. Write a set of parametric equations for the path of the football.
b. If Wilkins is punting the ball from the 48-yard line (43.9 meters) on the opponent's side
(48 yards from the end zone, which is 10 yards (9.14 meters) deep), will the ball land in
the end zone? What is the amount of time that the football is in the air for?
c. What is the maximum height of the football and at what time does this occur?
Chapter 8: Vectors
1. Use law of sin and law of cos in order to solve for the vector sum of two vectors.
[6, H160*]+[5, H60*]
Graph the solution, but also algebraically solve for the magnitude and direction.
2. Sam is flying an airplane with the speed of 570 mph in the direction of 45 degrees. If their is a
wind blowing in a direction of 180 degrees with a velocity of 160 mph, determine the velocity
and direction of the plane relative to the earth.
a. Graph the resulting vector and use algebra to solve for the magnitude and direction.
b. If a flock of birds takes up the entirety of quadrant one, will the plane hit them?
c. ​There is an alien spaceship that is pushing everything in the world by a magnitude of 70
in the direction of 270 degrees, when added does this change the answer for problem b?
Chapter 9: Polar
1. Determine the equation of each graph
a.
b.
c.
d.
2.
a. Convert the following problem/coordinate into polar form.
- (4, -2)
- (x + 4)2 + y 2 = 16
b. Convert the following problem/coordinate into rectangular form.
-
[6, 5π6 ]
-
r =− 4sinθ