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# Some Applications of Trigonometry class 10 Notes Mathematics

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## Chapter 9 Some Application of Trigonometry class 10 Notes

Download CBSE class 10th revision notes for Chapter 9 Some Applications of Trigonometry in PDF format for free. Download revision notes for Some Applications of Trigonometry class 10 Notes and score high in exams. These are the Some Applications of Trigonometry class 10 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the the best tips recommended by teachers during exam days.

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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## CBSE Class-10 Revision Notes and Key Points

Some Applications of Trigonometry class 10 Notes. CBSE quick revision note for Class-10 Mathematics, Chemistry, Maths, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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