12 SL: Antiderivatives

As I’m away on Monday, you’ll want to get a head start on antiderivatives, which are, in some sense, the opposite of derivatives. For example, if the derivative of \(x^2\) is \(2x\), then the antiderivative of \(2x\) is \(x^2+c\), where \(c\) is the constant of integration.

Read Section 18B, 18D, and 18E.1 (paying particular attention to the examples), and complete the following questions.

Exercise 18B questions 1–3
Exercise 18D questions 1–9, 11, 12
Exercise 18E.1 questions 1–3

Aim to complete most, if not all, of these questions before our next class.

11 HL: Solving Trigonometric Equations

Yesterday we discussed finding the general solution to a simple trigonometric equation. Try each of the questions below before our next class.

  1. Explain how the image shown below illustrates one of the results we discussed in the last class.
    Two points are shown on the circumference of the unit circle. Colour one red, and the other blue.
  2. Find the general solution to the equation \(\cos \theta = \frac{1}{2}\), expressing your answers as exact values.
  3. Find the general solution to the equation \(2\sin^2\theta -5\sin \theta = -2\).