Question

if sin theta = 11/61, find sec theta

Answer 1

Answer:

$sec\theta=\dfrac{61}{60}$

Step-by-step explanation:

Given,

$sin\theta=\dfrac{11}{61}$

To Find :-

$Value\:of\:sec\theta$

Solution :-

We know that :-

$sin\theta=\dfrac{opposite\:side}{hypotenuse}$

$\implies \dfrac{opposite\:side}{hypotenuse}=\dfrac{11}{61}$

Opposite side = 11 , hypotenuse = 61

We know that :-

$(hypotenuse)^2=(opposide\:side)^2+(adjacent\:side)^2$

$(61)^2=(adjacent\:side)^2+(11)^2$

Let , adjacent side be 'x'.

$3721 = x^2+121$

$x^2=3721-121$

$x^2=3600$

x = 60

Adjacent side = x = 60

$sec\theta=\dfrac{hypotenuse}{adjacent\:side}$

$sec\theta=\dfrac{61}{60}$

Know More :-

$1.\: sin\theta=\dfrac{opposite\:side}{hypotenuse}$

$2.\:cos\theta=\dfrac{adjacent\:side}{hyptenuse}$

$3.\:tan\theta=\dfrac{opposite\:side}{adjacent\:side}$

$4.\:csc\theta=\dfrac{hypotenuse}{opposite\:side}$

$5.\:sec\theta=\dfrac{hypotenuse}{adjacent\:side}$

$6.\:cot\theta=\dfrac{adjacent\:side}{opposite\:side}$