UPSKILL MATH PLUS

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Learn more### Theory:

Trigonometry (originated from Greek word

*trigonon*means*triangle*and*metron*means*measure*) is a branch of mathematics which deals with the study of relationship involving length of sides and angles of triangles.*Trigonometric Ratios*:

Consider a right-angled triangle with a corresponding angle \(\theta\).

In the figure, the side opposite to the given angle \(\theta\) is called the '

*Opposite side*', the side adjacent to the given angle \(\theta\) is called the '*Adjacent side*', and the greatest side opposite to right angle is called the '*hypotenuse*'.Important!

Click here! To recall the Pythagoras theorem. (Since we frequently make use of the right-angled triangle.)

Based on the given corresponding angle \(\theta\), we will learn about three basic trigonometric ratios satisfied by a right-angled triangle.

Each of these ratios is obtained by dividing one side of the right-angled triangle by another.

The three basic trigonometric ratios are:

**Sine****Cosine****Tangent**

The table below depicts the relation of these ratios with the right-angled triangle.

Name of the angle | Sine | Cosine | Tangent |

Short form of the angle | \(\sin\) | \(\cos\) | \(\tan\) |

Measurements related to the right-angled triangle | |||

Relationship | \(\sin \theta\) \(=\) \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\) | \(\cos \theta\) \(=\) \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\) | \(\tan \theta\) \(=\) \(\frac{\text{Opposite side}}{\text{Adjacent side}}\) |

Important!

**1.**The trigonometric ratios are unitless as they are defined in terms of ratios of sides of the triangle.

**2.**The ratios \(\sin \theta\), \(\cos \theta\) and \(\tan \theta\) should not be treated as \((\sin) \times (\theta)\), \((\cos) \times (\theta)\) and \((\tan) \times (\theta)\).