Which of the following situations best describes why excluding the value of a variable from the denominator of an algebraic fraction is necessary? the value of the variable makes the numerator zero. the value of the variable makes both the numerator and denominator zero. the value of the variable makes the denominator zero. the value of the variable makes the fraction equal to zero.

The right option is "The value of the variable makes the denominator zero".

Step-by-step explanation:

We have to find the option from the following situations that best describes why excluding the value of a variable from the denominator of an algebraic fraction is necessary.

The right option is "The value of the variable makes the denominator zero".

So, if the denominator of a function is zero, then the function becomes undefined and hence, we have to exclude that value of the variable which makes the denominator equals to zero. (Answer)

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)

answer: x

step-by-step explanation: