Simplifying Trig Expressions
Applications using logarithms
Converting logs, and exponential functions
Verifying Trig Identities
Double and Half angles
100
Cos(x)Sec(x)
1
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
100
Convert to exponential function logbase3(x)=2
3^2=x x=9
100
Sin(x)sec(x)=Tan(x)
Proofs will vary... Sin(x) 1/cos(x) Sin(x)/cos(x) Tan(x)
100
Find the exact value of Cos(75degrees)
(√6-√2)/4
200
Cos^2(x)/1-cos^2(x)
Cot^2(x)
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
200
Convert to exponential function logbase6(9)=x
6^x=9 x=1.22, or 61/50
200
Tan(x)cot(x)/sec(x)=cos(x)
Proofs will vary... Tan(x) 1/tan(x) 1/sec(x) Cos(x)
200
Find the exact value of sin42º cos12º-cos42º sin12º
1/2
300
[Tan(x)+1]/[sec(x)]
Sin(x)+cos(x)
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
300
Convert to logarithm 3^4=x
Log(x)base3=4
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)
300
Find exact value of sin105º
√(2+√3)/2
400
Cot(x)[Tan(x)+cot(x)]
Csc^2(x)
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
400
Convert to logarithm 2^x=7
logbase2(7)=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)
400
Find the exact value Cos4(x)
-79/81
500
[Sin^2(x)-tan^2(x)]/[tan^(x)sin^2(x)]
-1
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
500
Convert to exponential function logbase2(1 / 8) = -3
1/8 = 2^-3
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)
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 ]
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