3. TRIGONOMETRY
• As the name might suggest, is all about triangles.
• More specifically, trigonometry is about right-angled triangles, where one of the internal
angle is 90°.
• Trigonometry is a system that helps us to work out missing or known side
lengths or angles in a triangle.
ADJACENT
OPPOSITE
Trigonometry is a system that
helps us to work out missing or
known side lengths or angles
in a triangle.
4. • The right angle is indicated by the little box in the corner.
• The other angle that we (usually) know is indicated by
theta (𝜽).
• The side opposite the right angle, which is the longest
side is called hypotenuse.
• The side opposite is called the opposite.
• The side next to theta is which is not hypotenuse is called
adjacent.
5. PYTHAGORAS THEOREM
• Applied to only right angled triangles.
“The square on the hypotenuse is equal to the sum of the squares on
the other two sides”
6. b²
a²
PYTHAGORAS’ THEOREM
a² + b² = c²
So, if we know the length of two
sides of a triangle and we need to
calculate the third, we can use
pythagoras’ theorem.
However, if only one side of length
and one internal angles, then
pythagoras is no use and we need to
use trigonometry.
7. INTRODUCTION TO SINE,
COSINE, AND TANGENT
• There are three basic functions in trigonometry, each of which is one side of a
right-angled triangle divided by another.
The three functions are:
NAME ABBREVIATION RELATIONSHIP TO SIDE OF
THE TRIANGLE
SINE SIN SIN (𝜽) =
OPPOSITE/HYPOTENUS
E
COSINE COS COS (𝜽) =
ADJACENT/HYPOTENUS
E
TANGENT TAN TAN (𝜽) =
OPPOSITE/ADJACENT
9. TRIGONOMETRY IN A CIRCLE
When considering triangles, we
are limited to angles less than
90°. However trigonometry is
equally applicable to all angles,
from 0 to 360°. QUADRANT I
QUADRANT II
QUADRANT III QUADRANT IV
“ALL STUDENT TAKE
CALCULUS”
SINE ALL
COSINE
TANGENT
10. Trigonometry is said to be the most important
mathematical relationship ever discovered.
11. 1 PROBLEM-SOLVING
EXAMPLE
Ryan runs 4m, 40° north of east, 2m east 5.20m, 30° south of west and
6.50m south before stopping for water break. Find the resultant
displacement from where she started.
Given:
𝑨
= 4m, 40° north of east Find: Displacement
𝑩
= 2m of east
𝑪
= 5.20m, 30° south of west
𝑫
= 6.50m, south
12. 1.
𝑨
= 4M, 40° NORTH OF EAST
Cos 40= Ax/4m sin 40=Ay/4m
=4m(cos 40) =4m(sin 40)
=4m(0.77) =4m(0.64)
=3.08m =2.56m
40°
Ax=3.08m
Ay=2.56m
14. 3.
𝑪
= 5.20M, 30° SOUTH OF WEST
Cos 30°= Cx/5.20m sin 30°=Cy/5.20m
=5.20m(cos 30°) =5.20m(sin 30°)
=5.20m(0.87) =5.20m(0.5)
=-4.52m =-2.6m
30°
Cy=-2.6m
Cx=-4.52m
19. CONCLUSION
Trigonometry may not have all that many everyday applications,
but it does help you to work with triangles more readily. It’s a
useful supplement to geometry and actual measurements, and
as such well worth developing an understanding of the basics,
even if you never wish to progress further.
