CDS QUANT TRIGONOMETRY QUIZ 25

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Question 1:

Consider the following statement :-

(1) $\sin \theta$ is an increasing function of $\theta$ in the first quadrant

(2) $\cos \theta$ is an increasing function of $\theta$ in the first and second quadrant

(3) $0<\sin \theta<\cos \theta$, for $0<\theta<\frac{\pi}{4}$

(4) $\sin \theta<\cos \theta<0$, for $\frac{\pi}{4}<\theta<\frac{\pi}{2}$

Question 2:

Direction: Convert the decimal degrees to dgree, minutes and seconds.
$827.12^{\circ}$

Question 3:

Find the value. 

$\sin 22 \frac{1}{2}^{\circ}$

Question 4:

Find $\max ^{m}$ value of $\sin ^{4} \theta \cdot \cos ^{4} \theta$?

Question 5:

Let $A B C$ be a triangle right angled at $C$, then what is $\tan A+\tan B$ equal to?

Question 6:

If $\frac{\sec \theta+\tan \theta}{\sec \theta-\tan \theta}=\frac{5}{3}$, then, find the value of ' $\sin \theta$ '.

Question 7:

What is the ratio of the greatest to the smallest value of $2-2 \sin x-\sin ^{2} x$, $0 \leq x \leq \frac{\pi}{2} ?$

Question 8:

Find the value:-

$\sqrt{2+\sqrt{2+2 \cos 4 \theta}}$

Question 9:

Direction: Convert each of the following degree measure to radian measure.
$-70^{\circ}$

Question 10:

IF $x+y=135^{\circ}$ then find $\left(1+\tan \frac{x}{3}\right)\left(1+\tan \frac{y}{3}\right)$.