(C) Given that $\operatorname{cosec} \theta = \frac{2}{\sqrt{3}}$.Since $\operatorname{cosec} \theta = \frac{1}{\sin \theta}$,we have $\sin \theta = \

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(C) Given that $\operatorname{cosec} \theta = \frac{2}{\sqrt{3}}$.Since $\operatorname{cosec} \theta = \frac{1}{\sin \theta}$,we have $\sin \theta = \frac{1}{\operatorname{cosec} \theta} = \frac{\sqrt{3}}{2}$.We know from trigonometric standard values that $\sin 60^\circ = \frac{\sqrt{3}}{2}$.Comparing both sides,we get $\theta = 60^\circ$.

Class 10 Mathematics Introduction to Trigonometry Trigonometric Ratios of Some Specific Angles

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If $\operatorname{cosec} \theta = \frac{2}{\sqrt{3}}$,then $\theta = \ldots$ (in $^\circ$)

A
$30$
B
$45$
C
$60$
D
$90$

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Chapter

Introduction to Trigonometry

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Trigonometric Ratios of Some Specific Angles

In $\triangle ABC$,right-angled at $B$,$AB = 5 \, cm$ and $\angle ACB = 30^{\circ}$. Determine the lengths of the sides $BC$ and $AC$.

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In a right triangle,if the measure of one of the angles is $30^{\circ}$,then the side opposite to the angle with measure $30^{\circ}$ is .......... times the hypotenuse.

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In $\Delta ABC$,$m\angle B = 90^\circ$,$m\angle C = 30^\circ$ and $AC = 30 \text{ cm}$,then $AB = \ldots \text{ cm}$.

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For acute angle $\theta,$ if $\cos \theta = \sin \theta,$ then $2 \tan^{2} \theta + \sin^{2} \theta + 1 = \ldots$

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$\frac{2 \tan 30^{\circ}}{1-\tan ^{2} 30^{\circ}} = ?$

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If $\operatorname{cosec} \theta = \frac{2}{\sqrt{3}}$,then $\theta = \ldots$ (in $^\circ$)

Similar Questions

In $\triangle ABC$,right-angled at $B$,$AB = 5 \, cm$ and $\angle ACB = 30^{\circ}$. Determine the lengths of the sides $BC$ and $AC$.

In a right triangle,if the measure of one of the angles is $30^{\circ}$,then the side opposite to the angle with measure $30^{\circ}$ is .......... times the hypotenuse.

In $\Delta ABC$,$m\angle B = 90^\circ$,$m\angle C = 30^\circ$ and $AC = 30 \text{ cm}$,then $AB = \ldots \text{ cm}$.

For acute angle $\theta,$ if $\cos \theta = \sin \theta,$ then $2 \tan^{2} \theta + \sin^{2} \theta + 1 = \ldots$

$\frac{2 \tan 30^{\circ}}{1-\tan ^{2} 30^{\circ}} = ?$

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