FP1-Chapter-tFormulae Dr Frost What are 𝑡-formulae, and why use?

Statistics- What are 𝑡-formulae, and why use?

1. [email protected] www.drfrostmaths.com @DrFrostMaths Last modified: 1 st November 2020 Further Pure 1 Chapter 5 :: The -formulae  

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3. What are -formulae, and why use?   ! -formulae are writing trigonometric functions in terms of When   In this chapter we’ll see how we can use -formulae for solving equations and proving trigonometric identities . However, in practice they are seldom used for this purpose – they become much more useful in integrating more complicated trigonometric expressions ( Chp 7), just like we use double angle formulae to determine integrals like , and .   Proof using a Triangle         ? ? ? ?       Hint : Double angle formulae? ? ? ? (proof applicable to acute only)  

4. What are -formulae, and why use?   ! -formulae are writing trigonometric functions in terms of When   Proof using trig identities only:   Hint : We want everything in terms of or (as for the latter we can use an identity to turn into tan)       As before. ? ?

5. Simple use of the -formulae   When   [Textbook] Given that , determine the value of: (a) (b)       ?

6. Simple use of the -formulae   When   [Textbook] Given that and , find: the exact value of the value of , correct to 3 significant figures.   Use   a b When square rooting, we have a choice of + or . Since is obtuse, will be negative.   ? Calculate first       ? ?

7. Exercise 5A Pearson Further Pure 1 Pages 119-120

8. Applying -formulae to trig identities   [Textbook] Prove that , ,   Let   When   ? LHS ? RHS

9. Applying -formulae to trig identities   [Textbook] Prove that , ,   When   Let   Because we’re dealing with and instead of and , use for instead of   ? LHS ? RHS ? ? ?

10. Exercise 5B Pearson Further Pure 1 Pages 121-122

11. Solving trig equations [Textbook] Solve for   When   Let Solving this gives (2dp) and (2dp)   A better way of solving this would be to use the expansion of ) (Pure Year 2)   Strategy : Get equation in terms of in the hope it’s easier to solve, then replace back for at the end.   ?

12. Test Your Understanding ? ? Edexcel FP1 Specimen Paper

13. Exercise 5C Pearson Further Pure 1 Pages 123-124

14. Modelling with trigonometry [Textbook] The displacement of a particle moving in a straight line, m, at time seconds is given by Show that the velocity of the particle at time seconds is given by , ms -1 , where Hence find the value of where for which the displacement is maximised.   When   Differentiating: Use the second derivative to work out which of these solutions gives a maximum. This occurs when   ? Trig functions in general model many things with periodic behaviour , e.g. tides, daylight hours. We can use -formulae to help us solve such equations.   We’re using rather than So And   a b ?

15. Exercise 5D Pearson Further Pure 1 Pages 125-126