Trigonometric Ratios of Standard Angles

Find the value (in mixed fraction form) of the following: ${\sin }^2 30°+{\cos }^2 60°+\mathrm{cosec} 30°$

Find the value of the following: $\tan 30°\times \tan 60°+\cos 0°+\sec 60°$

Find $\mathrm{\theta }$(in $°$) if $0°<\mathrm{\theta }\le 90°$: $\sin \mathrm{\theta }=2 \sin 30°\cos 30°$.

Find $\mathrm{\theta }$(in $°$) if $0°<\mathrm{\theta }\le 90°$: $\cos \mathrm{\theta }={\cos }^2 30°-{\sin }^2 30°$.

Find $\mathrm{\theta }$(in $°$) if $0°<\mathrm{\theta }\le 90°$: $\left( {\tan }^2 \mathrm{\theta }-3 \right)\left(2 \sin 3\mathrm{\theta }-1\right)=0$.

Find $\mathrm{\theta }$(in $°$) if $0°<\mathrm{\theta }\le 90°$: $3 {\tan }^2 \left(\mathrm{\theta }+10°\right)=1$.

If$\sin \mathrm{\theta }=0.96$, find the value of $\cot \mathrm{\theta }+\mathrm{cosec} \mathrm{\theta }$.

Do as directed:

$2 {\cos }^2 \mathrm{\theta }-1=0,$ find $\mathrm{\theta }, \tan \mathrm{\theta }, \sin 2\mathrm{\theta } \mathrm{and} {\sin }^2 \mathrm{\theta }$.

Find the measure of angle $\mathrm{\theta }$ in the following when $\mathrm{\theta }$ is acute.(in $°$) :

$2 \sin \mathrm{\theta }-1=0$ show that $\sin 3\mathrm{\theta }=3 \sin \mathrm{\theta }-4 {\sin }^3 \mathrm{\theta }$.

Find the measure of angle $\mathrm{\theta }$ in the following when $\mathrm{\theta }$ is acute.(in $°$) :

$3 {\tan }^2 \mathrm{\theta }=1$. Show that $\frac{2 \tan \mathrm{\theta }}{1-{\tan }^2 \mathrm{\theta }}=\tan 2\mathrm{\theta }$.

Find the measure of angle $\mathrm{\theta }$ in the following when $\mathrm{\theta }$ is acute.(in $°$) :

$4 {\cos }^2 \mathrm{\theta }-3=0$ show that $4 {\cos }^3 \mathrm{\theta }-3 \cos \mathrm{\theta }= \cos 3\mathrm{\theta }$

Find the measure of angle $\mathrm{\theta }$ in the following when $\mathrm{\theta }$ is acute.(in $°$) :

$\tan 3\mathrm{\theta }-1=0$

Find the measure of angle $\mathrm{\theta }$ in the following when $\mathrm{\theta }$ is acute.(in $°$) :

$2 {\cos }^2 5\mathrm{\theta }=1$

Find the measure of angle $\mathrm{\theta }$ in the following when $\mathrm{\theta }$ is acute.(in $°$) :

 $\sin \left(\frac{\mathrm{\theta }}{3}+10°\right) =\frac{1}{2}$.

Find $\mathrm{\theta }$(in $°$) if $0°<\mathrm{\theta }\le 90°$: ${\sin }^{2 }\mathrm{\theta }+{\cos }^2 30° =\frac{5}{4}$.

Find $\mathrm{\theta }$(in $°$) if $0°<\mathrm{\theta }\le 90°$: $\cos \mathrm{\theta }=\cos 60° \cos 30°+\sin 60° \sin 30°$.

Find $\mathrm{\theta }$(in $°$) if $0°<\mathrm{\theta }\le 90°$: $\sin \mathrm{\theta }=3 \sin 30°-4 {\sin }^3 30°$.

Find $\mathrm{\theta }$(in $°$) if $0°<\mathrm{\theta }\le 90°$: $\tan \mathrm{\theta }=\sin 30°\cos 60°+\cos 30°\sin 60°$.

Find $\mathrm{\theta }$(in $°$) if $0°<\mathrm{\theta }\le 90°$: $\cos \mathrm{\theta }=4 {\cos }^{3 }30°-3 \cos 30°$.

Find $\mathrm{\theta }$(in $°$) if $0°<\mathrm{\theta }\le 90°$: $\sin \mathrm{\theta }=\frac{2 \tan 30°}{1+{\tan }^2 30°}$.