1 Answer

Salvationishere · Answer 1 · 2021-09-21T04:05:41+0000

The value of
$\csc \theta$ is
(5)/(4)

Step-by-step explanation:

Given that the function
$cos \ \theta$ is
$cos \ \theta= (3)/(5)$

We need to determine the value of
$\csc \theta$

The value of Opposite side of the triangle:

The formula for
$cos \ \theta$ is given by

$cos \ \theta= (adj)/(hyp)=(3)/(5)$

The value of opposite side can be determined using the formula,

$opp=\sqrt{hyp^2-adj^2$

opp=√(5^2-3^2)

opp=√(25-9)

opp=√(16)=4

Thus, the value of opposite side is 4

The value of
$\csc \theta$ :

The formula for
$\csc \theta$ is given by

$csc \ \theta=(1)/(sin \ \theta)$

First, we shall determine the value of
$sin \ \theta$

The formula for
$sin \ \theta$ is given by

$sin \ \theta= (opp)/(hyp)$

Substituting the values, we have,

$sin \ \theta= (4)/(5)$

Thus, the value of
$sin \ \theta$ is
(4)/(5)

Substituting the values in the formula for
$\csc \theta$ , we have,

$csc \ \theta=(1)/((4)/(5))$

$csc\ \theta= (5)/(4)$

Hence, the value of
$\csc \theta$ is
(5)/(4)

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