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Chapter 9 Some Application of Trigonometry class 10 Notes

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CBSE Class 10 Math
Revision Notes
CHAPTER 09
Some Application of Trigonometry class 10 Notes

1. Heights and Distances
2. Miscellaneous Questions

1. Trigonometric Ratios: In $\Delta ABC$ , $\angle B = {90^o}$ , for angle ‘A’

$sin\;A\; = \;\frac{{Perpendicular}}{{Hypotenuse}}$

$cos\;A = \;\frac{{Base}}{{Hypotenuse}}$

$\tan \;A\, = \;\frac{{\operatorname{P} erpendicular}}{{Base}}$

$cot\;A = \;\frac{{Base}}{{Perpendicular}}$

$sec\;A\, = \;\frac{{Hypotenuse}}{{Base}}$

$cosec\;A\, = \;\frac{{Hypotenuse}}{{Perpendicular}}$

2. Reciprocal Relations :

$\sin \theta = \frac{1}{{cosec\;\theta }}$ , $cosec\;\theta = \frac{1}{{\sin \theta }}$

$\cos \;\theta = \frac{1}{{sec\;\theta }}$ , $sec\;\theta = \frac{1}{{\cos \theta }}$

$\tan \;\theta = \frac{1}{{\cot \;\theta }}$ , $\cot \;\theta = \frac{1}{{\tan \theta }}$

3. Quotient Relations :

$\tan \theta = \frac{{\sin \theta }}{{\cos \theta }}$ , $\cot \theta = \frac{{\cos \theta }}{{\sin \theta }}$

4. Indentities:

(a) $\begin{gathered} {\sin ^2}\theta + {\cos ^2}\theta = 1 \\ \Rightarrow {\sin ^2}\theta = 1 - {\cos ^2}\theta \\ \Rightarrow {\cos ^2}\theta = 1 - {\sin ^2}\theta \\ \end{gathered}$

$\Rightarrow$ $\sin \theta = \sqrt {1 - {{\cos }^2}\theta }$

$\Rightarrow$ $\cos \theta = \sqrt {1 - sin ^2\theta }$

(b) $\begin{gathered} 1 + {\cot ^2}\theta = \cos e{c^2}\theta \\ \Rightarrow {\cot ^2}\theta = \cos e{c^2}\theta - 1 \\ \Rightarrow co{\sec ^2}\theta - {\cot ^2}\theta = 1 \\ \end{gathered}$

$\Rightarrow$ $\cot \theta = \sqrt {\cos e{c^2}\theta - 1}$

$\Rightarrow$ $\cos ec\theta = \sqrt {1 + {{\cot }^2}\theta }$

(c) $\begin{gathered} 1 + {\tan ^2}\theta = {\sec^2}\theta \\ \Rightarrow {\tan ^2}\theta = {\sec^2}\theta - 1 \\ \Rightarrow {\sec ^2}\theta - {\tan ^2}\theta = 1 \\ \end{gathered}$

$\Rightarrow$ $\tan \theta = \sqrt {\sec{^2}\theta - 1}$

$\Rightarrow$ $\sec\theta = \sqrt {1 + {{\tan }^2}\theta }$

5.Trigonometric Ratios of Some Specific Angles

6. Trigonometric Ratios of Complementary Angles

$\sin \;({90^o} - \theta ) = \;\cos \;\theta$

$\cos\;({90^o} - \theta ) = \;\sin \;\theta$

$\tan \;({90^o} - \theta ) = \;\cot \;\theta$

$\cot \;({90^o} - \theta ) = \;\tan \;\theta$

$\sec \;({90^o} - \theta ) = \;cosec\;\theta$

$cosec\;({90^o} - \theta ) = \;\sec \;\theta$

1. Line of Sight : The line of sight is the line drawn from the eyes of an observer to a point in the object viewed by the observer.

2. Angle of Elevation : The angle of elevation is the angle formed by the line of sight with the horizontal, when it is above the horizontal level i.e., the case when we raise our head to look at the object.

3. Angle of Depression : The angle of depression is the angle formed by the line of sight with the horizontal when it is below the horizontal i.e., case when we lower our head to look at the object.

Some Application of Trigonometry class 10 Notes

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