Geometry 8.3 Trignometric Ratios - Sin θ, Cos θ and Tan θ
Introduction:
Right triangles are of importance in geometry. Thus, mathematicians have developed a shorthand for writing the ratios of the sides of right triangles.
Instead of writing "the ratio of the leg adjacent to an 18 degree angle to the hypotenuse of the triangle" we write cos 18.
Because expression of this type frequently come up in physics, engineering and many other branches of science, such a shorthand was developed.
Sine, Cosine, Tangent of an Angle
In the right angled triangle ΔPAB, ∠PAB = θ
Then the ratio
PB/AP is called the sine of angle θ.
It is written as
In other form
Note : If ∠APB = φ then
AB/AP is called the cosine of angle θ
It is written as
In other form
Note : If ∠APB = φ then
PB/AB is called the tangent of angle θ.
It is written as
In the other form
or
An easy way to remember these relationships for trig functions and the right triangle is given below
Write down this mnemonic: SOH - CAH - TOA
It is pronounced "so - ka - toe - ah".
The SOH stands for "Sine of an angle is Opposite over Hypotenuse."
The CAH stands for "Cosine of an angle is Adjacent over Hypotenuse."
The TOA stands for "Tangent of an angle is Opposite over Adjacent". Directions: Answer the following questions. Also write at least 10 examples of your own.