Download presentation

Presentation is loading. Please wait.

1
Trigonometry (1) Sine Rule Cosine Rule

2
[Height] h2 = b2 - x2 [Height] h2 = a2 - (c-x)2 h2 = a2 - c2 +2cx - x2 C b2 - x2 = a2 - c2 +2cx - x2 +x2 +x2 a b2 = a2 - c2 +2cx b h b2 = a2 - c2 +2c x b cos A a2 = b2 + c2 - 2bc cos A B A x c-x c cos A = Adj/Hyp = x/b x = b cos A The cosine rule proof - won’t be examined

3
**The Cosine Rule a2 = b2 + c2 - 2bc cos A b2 = a2 + c2 - 2ac cos B**

… is used for working out angles and sides in non-right angled triangles a2 = b2 + c2 - 2bc cos A It is …. C angles a sides b A B c By similar proofs:- b2 = a2 + c2 - 2ac cos B c2 = a2 + b2 - 2ab cos C

4
**The Cosine Rule - example**

Finding a side a2 = b2 + c2 - 2bc cos A C angles sides 6 a ? 75o A B 8 a2 = x6x8 cos 75 a2 = x a2 = a =8.67 cm [2 d.p.]

5
**The Cosine Rule - example**

Finding an angle a2 = b2 + c2 - 2bc cos A C angles sides 7.1 13.5 ? A B 8.8 13.52 = x7.1x8.8 cos A 2x7.1x8.8 cos A = cos A = = 2x7.1x8.8 A = 116o [to nearest degree]

6
**Turn to page 71 of your Core 2 book and answer …**

Activity Turn to page 71 of your Core 2 book and answer … exercise B 1a) 2a)

7
sin A = Opp/Hyp = h/b C h = b sin A sin B = Opp/Hyp = h/a h = a sin B a If the perpendicular was here b h h = b sin A = a sin B B sin A sin B a = b A c The sine rule proof - won’t be examined sin B sin C b = c

8
**The Sine Rule It is …. a = b = c sin A sin B sin C C angles a sides b**

… is used for working out angles and sides in non-right angled triangles It is …. a = b = c sin A sin B sin C C angles a sides b A B c

9
**The Sine Rule - example a = b = c sin A sin B sin C a = b a = 4**

Finding a side a = b = c sin A sin B sin C C angles sides 4 cm a ? 75o 35o A B a = b sin A sin B a = 4 sin sin 75 a = x sin 35 = = 2.4 cm [1dp] sin 75

10
**The Sine Rule - example a = b = c sin A sin B sin C a = b 4 = 6.5**

Finding an angle a = b = c sin A sin B sin C C angles sides 6.5 cm 4 cm 85o ? A B a = b sin A sin B = sin A sin 85 4 x sin 85 = x sin A sin A = 4 x sin 85 = 6.5 A = 38o or = 162o

11
**Turn to page 74 of your Core 2 book and answer …**

Activity Turn to page 74 of your Core 2 book and answer … exercise C 1a) 3a)

Similar presentations

OK

$100 $200 $300 $400 $500 $200 $300 $400 $500 Geometric mean Pythagorean Thm. Special Right Triangles Law of Sines and Cosines Trigonometry Angles of.

$100 $200 $300 $400 $500 $200 $300 $400 $500 Geometric mean Pythagorean Thm. Special Right Triangles Law of Sines and Cosines Trigonometry Angles of.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on french revolution class 9 Ppt on power diode rectifier Tcp fast open ppt on mac Ppt on ill effects of intoxicating substances supply act Ppt on regional trade agreements example Ppt on endangered species of plants and animals Ppt on landing gear system of an aircraft Ppt on ready to serve beverages recipes Ppt on charge-coupled device images Vlsi physical design ppt on high level synthesis