2. Using Trigonometric Ratios (Sine, Cosine, Tangent)

Trigonometry

Trigonometry can be simply described as the study of triangles.
In this unit, we will be looking at two main areas:
SECTION 1: Right-angled Triangles
SECTION 2: Similar Triangles

SECTION 1

1. Using Pythagorean Theorem (a2+b2=c2)

2. Using Trigonometric Ratios (sine, cosine, tangent)

1. Using Pythagorean Theorem (a2+b2=c2)

·  Used when given 2 sides and asked to find the 3rd side. (Note: no angles involved)

Example 1: Example 2:

a2+b2=c2 a2+b2=c2

32+42=x2 62+x2=102

3 x 9 + 16=x2 6 10 36+x2=100

25 = x2 x2 = 100 – 36

x x2 = 64

5 = x

x = 8

2. Using Trigonometric Ratios (sine, cosine, tangent)

Used when trying to find either an unknown side or an unknown angle on a right-triangle.

Given (at least): 1 angle & 1 side à find unknown side

0 angle & 2 side à find unknown angle

Example1: Example2:

Use tan Use tan

tan q = tan q =

3 tan q = tan 25o =

5  tan q = 0.6 6 (tan 25o) = () 6

q = tan-10.6 2.8 = x

q = 30.9o x

(31o)

Example3:

Use sin

sin q =

sin 48o =

5  x =

x = 6.7