Question

if Sin A = to 1/2, then find the value of sec A, cosec.​

Answer 1

Sec A = 2 and Cosec A = 2/√3  

GIVEN :

Sin A = 1/2

TO FIND :

The value of Sec A, Cosec A.  

SOLUTION :

Given  Sin A = 1/2

From trigonometric table Sin 30 = 1/2

⇒  Sin A =  Sin 30°  

⇒  A = 30°

** Note: Cos 30° = √3/2**

⇒ Sec A = Sec 30°

As we know Sec θ = 1/Cosθ

⇒ Sec 30° = 1/Cos 30°

= 1/(√3/2)  = 2/√3

⇒ Sec 30° = 2/√3  

⇒ Cosec A = Cosec 30°

As we know Cosec θ = 1/Sinθ

⇒ Cosec 30° = 1/Sin 30°

= 1/(1/2)  = 2

⇒ Cosec 30° = 2  

Sec A = 2 and Cosec A = 2/√3

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Answer 2

Answer:

The answer to the given question is Sec A is

$\frac{ 2 }{ \sqrt{3} }$

cosec A =

$2$

Step-by-step explanation:

Given :

Sin A = 1/2

To find :

The value of sec A, cosec A.

Solution :

The value of sin A is given as 1/2.

we have to find the value of A.

from the trigonometric table, The value of A for which the sin value is 1/2 is 30°.

$\sin(30) = \frac{1}{2}$

Therefore, the value of A is 30°.

The value of cos 30°= √3/2.

sec A = sec 30°

It is known that the value of sec A =

$\frac{1}{ \cos(a) }$

Then

$\sec(30) = \frac{1}{ \cos(30) }$

$\frac{1}{ \frac{ \sqrt{3} }{2} } = \frac{2}{ \sqrt{3} }$

Therefore, the value of sec 30°=

$\frac{2}{ \sqrt{3} } .$

Cosec A = Cosec 30°

It is known that the cosec value is the reciprocal of the sin value.

Cosec A = 1/Sin A.

Cosec 30°= 2

$\csc(30) = \frac{1}{ \sin(30) } \\ = \frac{1}{ \frac{1}{2} } = 2$

Therefore, the final answer to the given question is

secA = 2/√3 and cosec A= 2.

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