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Introduction
Introduction
Earlier we covered Right Triangles and Pythogatian Theorem. This lesson covers the basics of Trigonometry and will review Pythagoras Theorem and introduce the basic concepts of Trigonometry: Sine, Cosine and, Tangent.
Right Triangle: Review
Right Triangle: Review
A right-angled triangle (also called a right triangle) is a triangle with a right angle (90°) in it.
The little square in the corner tells us it is a right-angled triangle.
Pythagorean Theorem: Review
Pythagorean Theorem: Review
Pythagorean Theorem establishes the relationship among the sides of right triangles. The theorem states that...
c2 = a2 + b2
Where c = hypotenuse, a and b represent the legs of the triangle.
Trigonometry establishes a relationship between the angles of a right triangle with its sides. Trigonometry shows these relationships by introducing six (6) functions called Trig functions. In this lesson we will cover the first six (3):
Sine,
Cosine, and
Tangent
These three trig ratios show the link between the sides and angles of the right triangle. We will need a better way to name the sides of the right triangle besides hypotenuse and legs.
Firstly, we will need to name the sides of the right triangle as Opposite, Adjacent, and Hypotenuse. We already know what the Hypotenuse is from previous lessons.
Hypotenuse: the longest side of the right triangle or the side in front of the right 90-degree angle.
The opposite and the Adjacent depend on the angle we are focussing on.
SOHCAHTOA Explained
SOHCAHTOA Explained
Sine, Cosine, and Tangent are the three main functions in trigonometry.
They are often shortened to sin, cos, and tan.
The calculation is simply...
one side of a right-angled triangle divided by another side
... we just have to know which sides, and how to apply "sohcahtoa".
For a triangle with an angle θ, the functions are calculated as shown in the diagram to the left.
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