DAY 86 INTRODUCTION TO TRIGONOMETRIC RATIOS INTRODUCTION The

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DAY 86 – INTRODUCTION TO TRIGONOMETRIC RATIOS

DAY 86 – INTRODUCTION TO TRIGONOMETRIC RATIOS

INTRODUCTION The word trigonometry is coined from two Greek words, trigonon meaning ‘triangle’ and

INTRODUCTION The word trigonometry is coined from two Greek words, trigonon meaning ‘triangle’ and metron meaning ‘measure’. Trigonometry is a branch of mathematics that explores the relationships between the sides and angles of triangles and the related calculations. Trigonometry is applied in several fields which deal with measurements such as engineering, architecture, surveying, navigation among others to find unknown angles and lengths. In this lesson, we will study ratios of the lengths of sides of a right triangle with reference to its acute angles and define trigonometric ratios of angles.

VOCABULARY Trigonometric ratio The ratio of the length of any two sides of a

VOCABULARY Trigonometric ratio The ratio of the length of any two sides of a right triangle with respect to a related angle.

SIDES AND ANGLES OF A RIGHT TRIANGLE A right triangle has one right angle

SIDES AND ANGLES OF A RIGHT TRIANGLE A right triangle has one right angle and two acute angles. Each of its three sides is given a special name. Its longest side is always opposite the right angle, and it is referred to as the hypotenuse. The other two sides, namely the opposite sides and the adjacent sides are named with respect to the acute angle under consideration in the triangle. The adjacent side and the opposite side change depending on the reference angle. Every acute angle is between two sides, the hypotenuse and one of the legs.

NAMING THE SIDES OF A RIGHT TRIANGLE A B C

NAMING THE SIDES OF A RIGHT TRIANGLE A B C

BASIC TRIGONOMETRIC RATIOS

BASIC TRIGONOMETRIC RATIOS

 P Q R

P Q R

From the definitions above, it is evident that: Sine is ‘Opposite over Hypotenuse’ Cosine

From the definitions above, it is evident that: Sine is ‘Opposite over Hypotenuse’ Cosine is ‘Adjacent over Hypotenuse’ and Tangent is ‘Opposite over Adjacent’ We can easily remember this ratios using the acronym SOH CAH TOA.

 P Q R

P Q R

 K L M

K L M

HOMEWORK P M N

HOMEWORK P M N

ANSWERS TO HOMEWORK MP is the hypotenuse NP is the adjacent side MN is

ANSWERS TO HOMEWORK MP is the hypotenuse NP is the adjacent side MN is the opposite side

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