Question

If sec theta=13/2 then find sin theta​

Answer 1

Step-by-step explanation:

sec theta= 13/2 ,cos = 2/13

sin theta = ??

sin^2 theta +cos^2 theta = 1

sin^2 theta + (2/13)^2 = 1

sin^2 theta + 4/169 = 1

sin^2 theta = 1-4/169

sin^2 theta = 169-4 /169

sin^2 theta = 165/169

sin theta =√165/169

sin theta = √165/13

Answer 2

Question:-

If sec theta=13/2 then find sin theta

Solution:-

Given,

$\sec(a) = \frac{13}{2} = \frac{hypotenuse}{adjacent \: side}$

So,

Hypotenuse = 13 cm

Adjacent Side = 2 cm

By pythagoras theorem,

${(hypotenuse)}^{2} = {(side)}^{2} + {(side)}^{2}$

Let opposite side = x

So,

${13}^{2} = {2}^{2} + {x}^{2}$

$169 = 4 + {x}^{2}$

$169 - 4 = {x}^{2}$

$165 = { x}^{2}$

$x = \sqrt{165}$

Then,

$\sin(a) = \frac{opposite \: side}{hypotenuse}$

$\sin(a) = \frac{ \sqrt{165} }{13}$