Lecture notes
Trigonometry Basics
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This notes helps the 10th students to score a good marks in the exam
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Trigonometry can help you find the height of a tall building like the Burj Khalifa withoutgoing to the top. You can also find the width of a river without using a long tape. Check out
our video on heights and distances for more information.
Pythagoras Theorem
Remember Pythagoras theorem which states that in a right angle triangle, the square of
the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is
helpful in finding the third side of a right angle triangle when given the other two sides.
Trigonometry Ratios
Trigonometry deals with right angle triangles and their angles and sides. In a right angle
triangle, we have the hypotenuse, perpendicular, and base. These terms are important in
understanding the trigonometric ratios. Given an angle and a side, we can use
trigonometry to find the other sides and angles of the triangle.
Trigonometric Ratios in a Right Angle Triangle
In a right angle triangle, the longest side opposite to the 90-degree angle is called the
hypotenuse. The side that contains the 90-degree angle and the angle theta is called the
base, while the side opposite to the angle theta is called the perpendicular.
Sine theta is defined as the ratio of perpendicular by hypotenuse, or AB/AC.
Cos theta is defined as the ratio of base by hypotenuse, or BC/AC.
Tan theta is defined as the ratio of perpendicular by base, or AB/BC.
It's important to note that these ratios only apply to right angle triangles.
Reciprocal Ratios
There are also reciprocal ratios of the trigonometric ratios:
Cosecant (csc) theta is defined as the reciprocal of sine theta, or AC/AB.
Secant (sec) theta is defined as the reciprocal of cos theta, or AC/BC.
Cotangent (cot) theta is defined as the reciprocal of tan theta, or BC/AB.
Relation between Sine, Cosine, and Tangent
In a right angle triangle, sine, cosine, and tangent are related as follows:
Sine theta = perpendicular/hypotenuse = AB/AC
Cosine theta = base/hypotenuse = BC/AC
Tangent theta = perpendicular/base = AB/BC
Cosecant theta = hypotenuse/perpendicular = AC/AB
Secant theta = hypotenuse/base = AC/BC
Cotangent theta = base/perpendicular = BC/AB
It's important to note that the hypotenuse is always opposite to the 90-degree angle, the
base contains both the 90-degree and theta angles, and the perpendicular is opposite to
the theta ang
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