more triangle trigonometry questions

  1. Calculate the area of a regular octagon inscribed in a unit circle.
  2. In quadrilateral ABCD, AB=3, BC=4, CD=5, and DA=6. The length of diagonal BD is 7. Calculate the length of the other diagonal.
  3. From the top of an observation post that is 90 meters high, a ranger sights a campsite at an angle of depression of 10°. Turning in a different direction, the ranger sees another campsite at an angle of depression of 13°. The angle between these two sight lines is 35°. How far apart are the campsites?

Trigonometry Test 2 is on Tuesday!

There are 14 questions, broken down as follows.

3 graphing rational functions

2 simplifying logs

3 log equations

2 exponential equations

1 inverse function

1 graphing exponential function

1 graphing log function

1 write the equation of an exponential function given certain conditions

Here are some good review questions.

  1. Solve for x: \log_5(2x)=\log_5(x+1)-1
  2. Solve for x and express your solution as a ratio of natural logs: 3^{\frac{-x}{2}}=4^{x+1}
  3. Sketch the graph of f(x)=-\ln(x-4)+2
  4. Sketch the graph of f(x)=e^{\frac{-x}{3}+1}
  5. Sketch the graph of f(x)=\frac{(x+2)^2(x+1)}{(x-4)^3(x-6)}
  6. f(x) has a horizontal asymptote at y=5. Where is the asymptote for f^{-1}(x)?
  7. f(x)=-5^x+1. Write the equation for f^{-1}(x).
  8. Solve for x and express your solution as a ratio of natural logs: 3^x+2=10.
  9. Re-write as an exponential equation: \log_{64}4=\frac{1}{3}.
  10. Sketch the graph of f(x)=\frac{6x^2+19x-7}{2x+7}

Also study quizzes 2, 3, and 4.

Critical vocabulary for midterm

Can you define all these terms? Doing so should be excellent practice for the exam, as well as a chance to review topics we’ve focused on over the past six weeks.

Rational function

Exponential function

Logarithmic function

Asymptote

Zeroes

y-intercept

Logarithm

Inverse function

Logarithmic scale

Exponential growth

Exponential decay

Exponential growth rate

Exponential decay rate

Continuously compounded interest