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Trigonometric Ratios - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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Trigonometric Functions of Acute Angles is considered one of the most asked concept.
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32 Questions around this concept.
Solve by difficulty
The expression can be written as:
If $\sin \theta=x$, find $\tan \theta$ ? (Given $\theta$ is an acute angle)
$\text{If}\; \cos \theta =\frac{1}{2},\text{ find} \: C\! osec\, \theta$
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Find $\cot \theta$ for the following figure :
$A D=\frac{2}{3} A C ; A C=4 ; A B=6$
Find $\sin x$ for this figure :
A beach rescue helicopter at an altitude of 250 m from the surface of the sea finds two persons sinking in the sea. If the angle of depression for the persons in the opposite directions are $60^{\circ}$ and $30^{\circ}$, find the distance between the two persons.
Find the value of $\mathrm{sec}^{-1}(-2)$
$\sin 30^{\circ}-\tan 45^{\circ}+\sec 60^{\circ}=$
Concepts Covered - 2
Trigonometric Functions of Acute Angles
Trigonometric Functions of Acute Angles
We can define the trigonometric functions in terms of an angle t and the lengths of the sides of the triangle. The adjacent side (=x) is the side closest to the angle (Adjacent means “next to.”). The opposite side (=y) is the side across from the angle. The hypotenuse (=1) is the side of the triangle opposite the right angle.
Sine $\sin \mathrm{t}=\frac{\text { opposite }}{\text { hypotenuse }}$
Cosine $\quad \cos \mathrm{t}=\frac{\text { adjacent }}{\text { hypotenuse }}$
Tangent $\tan t=\frac{\text { opposite }}{\text { adjacent }}$
Reciprocal Functions: In addition to sine, cosine, and tangent, there are three more functions. These too are defined in terms of the sides of the triangle.
$\begin{aligned} & \text { Cosecant } \quad \csc t=\frac{\text { hypotenuse }}{\text { opposite }}=\frac{1}{\sin t} \\ & \text { Secent } \quad \sec t=\frac{\text { hypotenuse }}{\text { adjacent }}=\frac{1}{\cos t} \\ & \text { Cotangent } \quad \cot t=\frac{\text { adjacent }}{\text { opposite }}=\frac{1}{\tan t}\end{aligned}$
Since, the hypotenuse is the greatest side in a right-angle triangle, and
can never be greater than unity and $\text{cosect}$ and $\text{sect}$ can never be less than unity.
Trigonometric Ratios of some Special Angles
$\text { Trigonometric Ratios of some Special Angles }$
| $\text { Angle }$ | $0$ | $\frac{\pi}{6}$, or $30^{\circ}$ | $\frac{\pi}{4}$, or $45^{\circ}$ | $\frac{\pi}{3}$, or $60^{\circ}$ | $\frac{\pi}{2}$, or $90^{\circ}$ |
| $\text { Cosine }$ | $1$ | $\frac{\sqrt{3}}{2}$ | $\frac{\sqrt{2}}{2}$ | $\frac{1}{2}$ | $0$ |
| $\text { Sine }$ | $0$ | $\frac{1}{2}$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{3}}{2}$ | $1$ |
| $\text { Tangent }$ | $0$ | $\frac{\sqrt{3}}{3}$ | $1$ | $\sqrt{3}$ | $\text { Undefined }$ |
| $\text { Secant }$ | $1$ | $\frac{2 \sqrt{3}}{3}$ | $\sqrt{2}$ | $2$ | $\text { Undefined }$ |
| $\text { Cosecant }$ | $\text { Undefined }$ | $2$ | $\sqrt{2}$ | $\frac{2 \sqrt{3}}{3}$ | $1$ |
| $\text { Cotangent }$ | $\text { Undefined }$ | $\sqrt{3}$ | $1$ | $\frac{\sqrt{3}}{3}$ | $0$ |
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Trigonometric Functions of Acute Angles
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