1. Starter
Mobile phones are ok for this activity. Please pack them away once finished!
Using memory, technology, or your textbook, fill in the unit circle given. Make sure to label each of the following:
The four quadrants
The angle measures of each position in degrees
The angle measures of each position in radians
The exact (x, y) coordinate of each position

2. Solution
Quadrant II
Quadrant I
The unit circle is your best friend . If you haven’t memorised it by now, do so ASAP!
Quadrant III
Quadrant IV

3. Angle Addition Formulae
A2 Maths with Liz
10/12/2014

4. Objectives Prior Knowledge Learn the angle addition formulae for
Use these formulae to work out the sin, cos, and tan of tricky angles (in degrees).
Prior Knowledge
SOH CAH TOA
Trig identities from C1 and C2
Values from the unit circle

5. The six angle addition formulae are
These are given in the formula booklet, but it’s always good to memorise them.

6. When will I use these formulae?
When working out the exact value of tricky angles such as
When simplifying trig expressions or solving trig equations (we’ll get to this in a few lessons).

7. Use the figure below to derive the addition formula for sin(A + B)
Steps to finding length RV:
1. Find length PQ in terms of angle B.
2. Similarly, find length RQ.
3. Find length QU in terms of angle A.
4. Show that angle RQT is = angle A.
5. Hence, find length TQ.
6. Using your results from above, write an expression for TU, the distance between the horizontal lines.
7. Since RV is also the distance between the horizontal lines, TU = RV. Thus, complete the formula for sin(A + B).
We just need to find RV in terms of A and B.

8. Congrats! You’ve just derived the first angle addition formula!
Check out mymaths to see the other formulae derived step by step.

9. Example 1 Show that Solution:
Think of two angles we can easily work with (from unit circle) that add or subtract to 75˚. A B
Use the sin(A + B) formula to work out.
Simplify the right hand side.
Note: You must memorise these common angle values!

10. Example 2 Find the exact value of Solution:
Think of two angles we can easily work with (from unit circle) that add or subtract to 135˚. OR A B
Why should we use tan(180˚ – 45˚)?
Because tan 90 ˚ is undefined.
Use the tan(A – B) formula to work out.
Simplify the right hand side.

11. Mix & Mingle! Work with someone new!
TARSIA DOMINOES!
Mix & Mingle! Work with someone new!

12. Plenary
On your card, (a) summarise what you’ve learned today in at least 3 short statements, (b) name at least one C1 or C2 topic you plan to brush up on to improve with this new topic

13. Independent Study Pre-Mock Exam Mymaths.co.uk
Addition Formulae Revision
Addition Formulae Online Homework
Please copy, complete, and mark your work in your independent study book. Due by next lesson – Friday, Dec. 12th.
Pre-Mock Exam
Core 3 pre-mock exam will be held on Friday, December 12th. REVISE! REVISE! REVISE!!!!!!