Trigonometric Ratios MCQ - Practice Questions & Answers

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Trigonometric Functions of Acute Angles is considered one of the most asked concept.
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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, $\text{sint}$ and $\text{cost }$ 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 $90^{\circ}$
$\text { Cosine }$	$1$	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{1}{2}$	$0$
$\text { Sine }$	$0$	$\frac{1}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{3}}{2}$	$1$
$\text { Tangent }$	$0$	$\frac{\sqrt{3}}{3}$	$1$	$\sqrt{3}$	$\text { Undefined }$
$\text { Secant }$	$1$	$\frac{2 \sqrt{3}}{3}$	$\sqrt{2}$	$2$	$\text { Undefined }$
$\text { Cosecant }$	$\text { Undefined }$	$2$	$\sqrt{2}$	$\frac{2 \sqrt{3}}{3}$	$1$
$\text { Cotangent }$	$\text { Undefined }$	$\sqrt{3}$	$1$	$\frac{\sqrt{3}}{3}$	$0$