The mean of the values sin^2 10^{circ}, sin^2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given values are $\sin^2 10^{\circ}, \sin^2 20^{\circ}, \sin^2 30^{\circ}, \dots, \sin^2 90^{\circ}$.There are $9$ terms in total.Sum $= \sin^

Vedclass · Accepted Answer

$\frac{5}{9}$

Vedclass · Answer

(A) The given values are $\sin^2 10^{\circ}, \sin^2 20^{\circ}, \sin^2 30^{\circ}, \dots, \sin^2 90^{\circ}$.There are $9$ terms in total.Sum $= \sin^2 10^{\circ} + \sin^2 20^{\circ} + \sin^2 30^{\circ} + \sin^2 40^{\circ} + \sin^2 50^{\circ} + \sin^2 60^{\circ} + \sin^2 70^{\circ} + \sin^2 80^{\circ} + \sin^2 90^{\circ}$.Using $\sin(90^{\circ} - 	heta) = \cos 	heta$,we have $\sin^2 80^{\circ} = \cos^2 10^{\circ}$,$\sin^2 70^{\circ} = \cos^2 20^{\circ}$,$\sin^2 60^{\circ} = \cos^2 30^{\circ}$,and $\sin^2 50^{\circ} = \cos^2 40^{\circ}$.Sum $= (\sin^2 10^{\circ} + \cos^2 10^{\circ}) + (\sin^2 20^{\circ} + \cos^2 20^{\circ}) + (\sin^2 30^{\circ} + \cos^2 30^{\circ}) + (\sin^2 40^{\circ} + \cos^2 40^{\circ}) + \sin^2 90^{\circ}$.Since $\sin^2 	heta + \cos^2 	heta = 1$ and $\sin 90^{\circ} = 1$,Sum $= 1 + 1 + 1 + 1 + (1)^2 = 5$.Mean $= \frac{	ext{Total Sum}}{	ext{Number of terms}} = \frac{5}{9}$.

$x_i$	$3$	$6$	$10$	$12$	$7$	$15$
$f_i$	$3$	$4$	$2$	$8$	$13$	$10$

$x_i$	$5$	$15$	$25$	$35$	$45$	$55$
$f_i$	$12$	$18$	$27$	$20$	$17$	$6$

The mean of the values $\sin^2 10^{\circ}, \sin^2 20^{\circ}, \sin^2 30^{\circ}, \ldots, \sin^2 90^{\circ}$ is $........$

Similar Questions

$A$ school has four sections of chemistry in class $XII$ having $40, 35, 45$ and $42$ students. The mean marks obtained in chemistry test are $50, 60, 55$ and $45$ respectively for the four sections. The overall average of marks per student is:

If for some $x \in R$,the frequency distribution of the marks obtained by $20$ students in a test is:
Marks: $2, 3, 5, 7$
Frequency: $(x+1)^2, 2x-5, x^2-3x, x$
Then the mean of the marks is:

The median of the following frequency distribution is:

$x_i$ $3$ $6$ $10$ $12$ $7$ $15$

$f_i$ $3$ $4$ $2$ $8$ $13$ $10$

The reciprocal of the mean of the reciprocals of $n$ observations is their

Find the mean of the following frequency distribution:

$x_i$ $5$ $15$ $25$ $35$ $45$ $55$

$f_i$ $12$ $18$ $27$ $20$ $17$ $6$

Vedclass Test Series

Exam Paper Generator

Online Exam Module