State whether the following are true or false. Justify your answer.
The value of $\cos \theta$ increases as $\theta$ increases
State whether the following are true or false. Justify your answer.
The value of $\cos \theta$ increases as $\theta$ increases
$\cos 0^{\circ}=1$
$\cos 30^{\circ}=\frac{\sqrt{3}}{2}=0.866$
$\cos 45^{\circ}=\frac{1}{\sqrt{2}}=0.707$
$\cos 60^{\circ}=\frac{1}{2}=0.5$
$\cos 90^{\circ}=0$
It can be observed that the value of $\cos \theta$ does not increase in the interval of$0^{\circ}<\theta<90^{\circ}$
Hence, the given statement is false.
Similar Questions
Evaluate:
$\frac{\sin 18^{\circ}}{\cos 72^{\circ}}$
Evaluate:
$\frac{\sin 18^{\circ}}{\cos 72^{\circ}}$
If $A , B$ and $C$ are interior angles of a triangle $ABC ,$ then show that
$\sin \left(\frac{B+C}{2}\right)=\cos \frac{A}{2}$
If $A , B$ and $C$ are interior angles of a triangle $ABC ,$ then show that
$\sin \left(\frac{B+C}{2}\right)=\cos \frac{A}{2}$
Evaluate the following:
$\frac{\cos 45^{\circ}}{\sec 30^{\circ}+\operatorname{cosec} 30^{\circ}}$
Evaluate the following:
$\frac{\cos 45^{\circ}}{\sec 30^{\circ}+\operatorname{cosec} 30^{\circ}}$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\frac{\tan \theta}{1-\cot \theta}+\frac{\cot \theta}{1-\tan \theta}=1+\sec \theta \operatorname{cosec} \theta$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\frac{\tan \theta}{1-\cot \theta}+\frac{\cot \theta}{1-\tan \theta}=1+\sec \theta \operatorname{cosec} \theta$
$(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta)=..........$
$(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta)=..........$