The Cosine Rule

A triangle is constructed with sides of length 8 cm, 10 cm, and 3 cm. What is the measure of the angle opposite the side measuring 3 cm?

See if you can answer this question before tomorrow’s lesson.

Inverse Trigonometric Functions

Complete the following questions (concerning both the recently discussed compound– and double-angle identities and the inverse trigonometric functions) for the beginning of our lesson on Monday.

If you get stuck with any of these, see if you can find a similar example in the textbook (of course, yo can also post your questions here as usual).

Pages 333–335 questions 1, 4, 7, 9, 13

Pages 344–345 questions 3, 6, 9, 10, 13, 17, 21, 28, 34, 39 a)

Fun with Comparison Tests

Your challenge tonight is to come up with a series that can be shown to converge using (either version of) the comparison test. We’ll vote on the best example tomorrow. Here’s my entry.

\[\sum_{n=1}^\infty \frac{1}{2^n-n^2}\]

Models with Trigonometric Functions

Here’s the question we considered in today’s lesson. See how far you can get on this question tonight, and we’ll continue our discussion tomorrow.

The London Eye is 15 m off the ground, and has a diameter of 120 m. The London Eye completes one revolution every 30 minutes.

  1. Develop a function to model the height of a passenger on the London Eye t minutes after boarding a capsule.
  2. How far above ground would passengers in a capsule be after
    a. 10 minutes have passed?
    b. 25 minutes have passed?