Announcements & Reminders! Wednesday, 18th March, 2:05 – 4:10pm: “Calculus” Revision session (Core 1 and 2 integration & differentiation). If you haven’t reached your target grade in this topic, I expect you to attend! Friday, 20th March: Core 1, June 2010 Past Paper DUE Tuesday, 24th March: Core 2 Test over Triangle Trigonometry (Independent Study Task)

Solving Trig Equations 2 Involving Trig Identities AS Maths with Liz Core 2

Aims Previous Knowledge By the end of today’s lesson, you should be able to… Simplify trig expressions using trig identities Solve harder trig equations using identities Previous Knowledge Sketching the sin, cos, & tan curves Solving basic trig equations within a given interval

Trigonometric Identities You will need to memorise the following trig identities for Core 2… For all values of AND

Done!  Example 1 Solution: Show that Start with left hand side, and rearrange and/or substitute identities until you reach the statement on the RHS. Look at the statement we are trying to prove…we need to rewrite the problem in terms of cos. Our identity is: Done!  Rearrange… Replace & simplify!

Example 2 Done!  Solution: Show that Start with left hand side, and rearrange and/or substitute identities until you reach the statement on the RHS. We need to rewrite the problem in terms of sin. Our identity won’t work just yet because the cos isn’t squared. Substitute using identity Done! 

Example 3 Solution: Start by factorising. Continue solving… and Use graphing method from previous lesson to solve each. Next, solve this equation! Mark solution on graph & find other solutions in interval. Mark solution on graph & find other solutions in interval.

Example 4 Solution: This one is tricky because it has both sin and cos in it. Use your identities to get it all in terms of a single trig function. Solve this equation using graphing technique from previous lesson! Second solution:

Example 5

You try! (a) (b)

Example 6 – Hidden Quadratics

You try!

Example 7

Exam Question June 2013

Exam Question – working out

Exam Question – working out

Exam Question – working out

Part bii continued...

Mark Scheme

Mark Scheme

Set Homework Optional Practise Trigonometry & Integration Set Homework Due Tuesday, 31st March (Blocks: A, B, G) Due Wednesday, 1st April (Block D) TEST OVER TOPIC HELD ON ABOVE DUE DATES Optional Practise Core 2 Textbook: Pg. 239, Ex. 1D Core 2 Textbook: Pg. 396, Ex. 9C mymaths – Trig Equations 2 MEI WS - “AQA Core 2 Trig, Section 2: Trig identities and equations” (ALL Questions)