1. 𝑇𝑒𝑠𝑡 𝑇𝑜𝑚𝑜𝑟𝑟𝑜𝑤 𝑜𝑛 𝐶ℎ. 6 𝑠𝑒𝑐𝑠. 1,2,5 Row 2
Do Now
An investor deposits $50 on the first day of each month in an account that pays 3% interest, compounded monthly. What is the balance at the end of 2 years? (This type of investment plan is called an increasing annuity.)

2. Do now solution– Increasing Annuity
An investor deposits $50 on the first day of each month in an account that pays 3% interest, compounded monthly. What is the balance at the end of 2 years? (This type of investment plan is called an increasing annuity.) Solution: To find the balance in the account after 24 months, consider each of the 24 deposits separately. The first deposit will gain interest for 24 months, and its balance will be

3. Do now solution–Increasing Annuity
cont’d
The second deposit will gain interest for 23 months, and its balance will be The last deposit will gain interest for only 1 month, and its balance will be

4. Do now solution–Increasing Annuity
cont’d
The total balance in the annuity will be the sum of the balances of the 24 deposits. Using the formula for the sum of a finite geometric sequence, with A1 = 50(1.005) and r = 1.005, and n = 24, you have
Sum of a finite
geometric sequence
Substitute 50(1.005) for A1,
1.005 for r, and 24 for n.
Use a calculator.

5. Review Sheet Solutions
1. Given
use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.
2. Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
48.68 sq. units
3. A straight road makes an angle, A, of
with the horizontal. When the angle of elevation, B, of the sun is
a vertical pole beside the road casts a shadow 7 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.
7.33 feet

6. Review Sheet Solutions
4. Given ,
, and
use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places
5. Given ,
, and
use the Law of Cosines to solve the triangle for the value of c. Round answer to two decimal places.
18.95
6. Given ,
, and
use Heron's Area Formula to find the area of triangle
Round answer to two decimal places.
64.06 sq. units
Review Sheet Solutions
7. Find values for
such that the triangle has two solutions.
8. Find values for
such that the triangle has no solutions.
9. Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve the triangle.
Law of Cosine;

7. Law of Sines; No solution.
10. Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve the triangle. Round your answer to two decimal places.
Law of Sines; No solution
11. Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve the triangle. Round your answer to two decimal places.
Law of Sines;
12. Perform the operation and leave the result in trigonometric form.
13. Find the absolute value of the complex number
14. Perform the operation shown below and leave the result in trigonometric form.
15. Use DeMoivre's Theorem to find the indicated power of the following complex number.

8. Write the roots in trigonometric form.
16. Find the fourth roots of
17. Find the cube roots of the following complex number. Write each of the roots in standard form.
Write the roots in trigonometric form.
18. Find the trigonometric form of .
20. Find the standard form of the complex number shown below.
19. Find the trigonometric form of the complex number shown below.