Quarter 4 Project

Chapter 7 Topics

100

Find sin(3π/4), cos(3π/4), and tan(3π/4).

Sin= √2/2

cos= -√2/2

tan= -1

√=square root

200

If cos(0)<0 and sin(0)>0, in which quadrant does the angle 0 lie? What are the signs of sin(0), cos(0), and tan(0)

Angle 0 is in Quad. 2

sin(0)= POSITIVE

cos(0)= NEGATIVE

tan(0)= NEGATIVE

300

Find the height of a building if the angle of elevation is 35° and the horizontal distance from the observer to the building is 50 meters.

= 35.01

400

Find the angle 0 if tan(0)= 3/4

=36.87°

500

Given sin(30°)=1/2 and the hyp. is 12 units, find the length of the opposite side.

=6

600

For a right triangle with angle 0, where sin(0)=3/5, find the values of all six trigonometric ratios. 

sin(0)=3/5

cos(0)=4/5

csc(0)=5/3

tan(0)=3/4

sec(0)=5/4

cot(0)=4/3

Chapter 7 Part 2 (Ch 8) Topics:

100

Use the formula for the area of a triangle:A=1/2ab sin(C), given a=10, b=12, and C=40°, to find the area.

38.57

200

Solve for the missing sides and angles in the triangle, given A=30°, a=6, and b=8

Angle B= 41.41

Angle C= 108.59°

Side c= 11.41

300

Solve for angle C in the Law of Cosines equation c²=a²+b²-2ab cos(C), given a=7, b=5, and c=9

C= 95.7°

400

Use the Law of Cosines to solve for side c in the equation 

c²=a²+b²-2ab cos(c)

given a=8, b=10, and C=45°

Side c length= 14.49

500

Solve for side b in the equation sin(A)/a=sin(B)/b, if A=40°, B=60°, and a=12

Side b= 16.16

600

Given sin(A)/a=sin(B)/b, solve for angle B, if A=30°, a=5, and b=8

Angle B= 53.13°

Chapter 9 Topics

100

Solve for x:

log(x+3)=2

x=97

200

Solve the exponential equation for x: 

2^3x=8^x

x= π

π= PI

300

Expand the following logarithmic expression

log₂(8x²y)

3+2log(x)+log₂(y)

400

Condense the following logarithmic expression into a single log: log₃(4)+log₃(5)

log₃20

500

Convert the following exponential equation to its logarithmic form: 

5³=125

log₅(125)=3

600

Convert the following logarithmic equation to it's exponential form: log₂(32)=5

2⁵=32

Chapter 10 Topics

100

Solve the exponential equation for x:

4^x=20

1+1/2log₂(5)

200

Find the population after 5 years if the initial population is 500 and it grows at a rate of 10% per year:

P(t)=500(1.10)5

805 people

300

Solve for (x) using natural logarithms:

e^2x=10

x=1/2xIn(10)

OR

1.15129

400

Calculate the amount of money after 10 years if you invest $1,000 at an annual interest rate of 5%, compounded quarterly.  

$1643.62

500

Solve for the amount remaining after 6 years if the initial amount is 2,00 and the growth rate is 7% per year.

After 6 years= 2,999.38

600

Solve for the amount remaining after 3 years if an initial amount of 1,000 decays at a rate of 5% per year.

A(t)=1,00(.95)^t

857.38

Chapter 11 Topics

100

Find the area of a triangle with base 8 and a height of 12.

A= 48

200

Simplify this complex fraction:

3/x ÷ 4/y

3y/4x

300

Subtract the following rational expression:

5/x+2 - 3/x+2

2/x+2

400

Answer the following rational expression:

2/x+3 + 3/x+3

5/x+3

500

Divide the following rational expression:

4x/x-3 ÷ x+1/2x

8x²/x²-2x-3

600

Multiply the following rational expressions:

3x/x+1* x+1/2x

*= multiplication

= 3/2