Download IB Math SL Lesson 2

IB Math SL Lesson 2.3 and 2.4 (Part 1): Trigonometric Functions and the Sine Rule
I. Periodic Trigonometric Functions
A. In Lesson 2.1, trigonometric functions were defined as ratios of sides of right triangles.
Therefore, values of trigonometric functions were only available for right and acute angles.
B. But values of trigonometric functions less than 0° and greater than 90° and l can be defined in
ways that produce periodic functions when sin , cos  , and tan  are plotted against  .
(This plotting can be done with respect to degree measure, but usually it is done with respect
to radian measure.)
C. The Sine Function
1. Graph of y = sin 
y
-2
O
2

2

2

D. The Cosine Function
1. Graph of y = cos 
y
-2
O
E. The Tangent Function
1. Graph of y = tan 
y
-2
O
II. The Sine Rule
A.
A
b
c
B
a
C
B. Example: Find x.
o
65
35
o
72
x
C. The Ambiguous Case of SSA
1. Example: solve the triangle ABC in which AC = 7, BC = 12 and B = 30°.
a. Angle BAC is acute
b. Angle BAC is obtuse
A
A
7
o
7
B
o
B
30
12
C
30
12
C