Work through the list without notes or a calculator. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions. This topic is shared by Calculus AB and Calculus BC.
Understanding
- I can rewrite tan x, cot x, sec x and csc x in terms of sin x and cos x, and state where each is defined. (Guide: “The idea: rewrite, then use a rule you know”; Practice Q5(b))
- I can explain why these derivatives are valid only with x in radians. (Guide: “A note on notation”)
- I can explain why tan x is increasing on each interval of its domain, using sec²x ≥ 1. (Guide: “Reading the derivative on a graph”, Figure 1; Practice Q6(c))
Skills
- I can derive d/dx tan x and d/dx sec x with the quotient rule. (Guide: “Deriving d/dx tan x”, “Deriving d/dx sec x”)
- I can derive d/dx cot x and d/dx csc x with the quotient rule. (Guide: Worked example 1; Practice Q5(a))
- I can write down all four derivatives from memory, with the correct signs. (Guide: “The four results”; Practice Q1)
- I can evaluate these derivatives exactly at π/6, π/4 and π/3. (Guide: Worked example 1; Practice Q2, Q6(b))
- I can differentiate products and quotients that contain these functions. (Guide: Worked examples 2 and 3; Practice Q3, Q7)
- I can write the equation of a tangent line to a graph built from these functions. (Guide: Worked examples 1 and 2; Practice Q5(c), Q7(c))
Reasoning
- I can use 1 + tan²x = sec²x (or sin²x + cos²x = 1) to simplify a derivative. (Guide: Worked example 3; Practice Q4, Q7(a))
- I can choose whether to rewrite a function first or differentiate it as given. (Practice Q7(b))
- I can interpret a trig derivative in context, with units. (Practice Q6(b))
All ticked? Move on to Topic 3.1, The Chain Rule, or return to the Calculus AB roadmap or the Calculus BC roadmap.