Semester 2 Pre Calc. Mrs. Gaynor ~Ahzam Kasam~

Simplifying Trig Expressions

100

Cos(x)Sec(x)

1

200

Cos^2(x)/1-cos^2(x)

Cot^2(x)

300

[Tan(x)+1]/[sec(x)]

Sin(x)+cos(x)

400

Cot(x)[Tan(x)+cot(x)]

Csc^2(x)

500

[Sin^2(x)-tan^2(x)]/[tan^(x)sin^2(x)]

-1

Applications using logarithms

100

If 3000$is invested in an account for which interest is compounded continuously at a rate of 6 1/2%, find the amount of the investment at the end of 3 years.

A=3000•e^(.065•3) A=3645.933

200

If you deposit $100 into your savings account which earns a 5% yearly interest rate, how much is in your account after two years.

100(1.05^2)=100(1.1025)= $110.25

300

If you deposit R into your savings account which compounds interest every month, what is the expression for the amount of money in your account after 2 years if you earn an interest rate of i?

A=R[1+(i/12)]^2

400

Mrs.Gaynor opens a savings account and deposits $1000. The saving account gains 5% interest per year after 3 years, Mrs. Gaynor withdraws all of her money, and deposits it into another account with 6% interest per year. 2 year later she withdraws all her money. How much money does Mrs. Gaynor have after this 5 year period?

After first 3 years= $1157.63 After 2 more years = $1300.71

500

How many years does it take for $1000 to grow into $5000, when the $1000 is deposited into a savings account that has an annual compound interest rate of 3%

54.45 years

Converting logs, and exponential functions

100

Convert to exponential function logbase3(x)=2

3^2=x x=9

200

Convert to exponential function logbase6(9)=x

6^x=9 x=1.22, or 61/50

300

Convert to logarithm 3^4=x

Log(x)base3=4

400

Convert to logarithm 2^x=7

logbase2(7)=x

500

Convert to exponential function logbase2(1 / 8) = -3

1/8 = 2^-3

Verifying Trig Identities

100

Sin(x)sec(x)=Tan(x)

Proofs will vary... Sin(x) 1/cos(x) Sin(x)/cos(x) Tan(x)

200

Tan(x)cot(x)/sec(x)=cos(x)

Proofs will vary... Tan(x) 1/tan(x) 1/sec(x) Cos(x)

300

cos^2(x)= csc(x)cos(x)/tan(x)+cot(x)

[cos(x) sin(x)]/ 1/sin(x) cos(x) cos^2(x)/1 = cos^2(x)

400

1-sin(x)/cos(x)=cos(x)/1+sin(x)

1-sin(x)/cos(x) X 1+sin(x)/1+sin(x) 1-sin^2(x)/cos(x)(1 + sin x) cos(x)/1+sin(x)

500

sec(x)+tan(x)=cos(x)/1-sin(x)

cosx(1 + sin x)/(1-sin x) (1 + sin x) [1/cos(x)]+[sin(x)/cos(x)] =sec(x)+tan(x)

Double and Half angles

100

Find the exact value of Cos(75degrees)

(√6-√2)/4

200

Find the exact value of sin42º cos12º-cos42º sin12º

1/2

300

Find exact value of sin105º

√(2+√3)/2

400

Find the exact value Cos4(x)

-79/81

500

x is in quadrant 3, approximate sin (2 x) if cos (x) = - 0.2. Round your answer to two decimal places.

sin(x)= - √[ 1 - (- 0.2)2 ]