• The derivation of the trigonometric formulae 1, 2,3,4, 5, 6, 7,9 (Appendix)
1. cos2A + sin2A = 1
Proving Trigonometric Identity – (Sin squared + cos squared = 1) - Alison.com
Pythagorean trig identity from soh cah toa Khan
Pythagorean trig identity from unit circle Khan
2. sine formula: a/Sin A=b /Sin B=c /Sin C
Proving the Sine Rule - Alison.com
Proof: Law of sines Khan
3. cosine formula: a2 = b2 + c2 – 2 bc cos A
Proving the Cosine Rule - Alison.com
Proof of the law of cosines Khan
4. cos (A–B) = cos A cos B + sin A sin B
Proof from Youtube KeysToMaths1
5. cos (A+B) = cos A cos B – sin A sin B
Proof from Youtube KeysToMaths1
Proof of angle addition formula for cosine khan
6. cos 2A = cos2 A – sin2 A
Proof from Youtube KeysToMaths1
7. sin (A+B) = sin A cos B + cos A sin B
Proof from Youtube KeysToMaths1
Proof of angle addition formula for sine khan
9. tan (A+B) = tan A + tan B / 1 – tan A tan B
Proof from Youtube KeysToMaths1
1. cos2A + sin2A = 1
2. sine formula: a/Sin A=b /Sin B=c /Sin C
3. cosine formula: a2 = b2 + c2 – 2 bc cos A
4. cos (A–B) = cos A cos B + sin A sin B
5. cos (A+B) = cos A cos B – sin A sin B
6. cos 2A = cos2 A – sin2 A
7. sin (A+B) = sin A cos B + cos A sin B
8. sin (A–B) = sin A cos B – cos A sin B
9. tan (A+B) = tan A + tan B / 1 – tan A tan B
10. tan (A–B) = tan A – tan B / 1 + tan A tan B
11. sin 2A = 2 sin A cos A
12. sin 2A = 2 tan A / 1 + tan2 A
13. cos 2A = 1 – tan2 A / 1 + tan2 A
14. tan 2A = 2 tan A / 1 – tan2 A
15. cos2 A = ½ (1 + cos 2A)
16. sin2 A = ½ (1 – cos 2A)
17. 2 cos A cos B = cos (A+B) + cos (A–B)
18. 2 sin A cos B = sin (A+B) + sin (A–B)
19. 2 sin A sin B = cos (A–B) – cos (A+B)
20. 2 cos A sin B = sin (A+B) – sin (A–B)
21. cos A + cos B = 2 cos(A+B)/2 . cos(A-B)/2
22. cos A – cos B = – 2 sin(A+B)/2 . sin(A-B)/2
23. sin A + sin B = 2 sin(A+B)/2 . cos(A-B)/2
24. sin A – sin B = 2 cos(A+B)/2 . sin(A-B)/2
LCHL need to be able to derive: 1, 2, 3, 4, 5, 6, 7, 9
• The uses of the trigonometric formulae 1-24 (Appendix)
Circles and Pythagorean identities
Manipulating trig expressions with pythagorean identities
Addition and subtraction trig identities
Applying angle addition formulas
Understanding angle addition formulas
Law of sines and law of cosines word problems
videos Trigonometric identities