Question

3. sin 0 = opposite/hypotenuse and its reciprocal is csc 0, what is csc 0? A.opposite/hypotenuseB.hypotenuse/oppositeC.adjacent/hypotenuseD.hypotenuse/adjacent

Answer 1

Csc 0 is Hypotenuse / opposite

Option B

Step-by-step explanation

Given information

`\text{ Sin 0 = }(opposite)/(Hypotenuse)`

To find the reciprocal of sin 0, follow the steps below

Step 1: Apply the SOH CAH TOA principle

`\begin{gathered} \text{ sin 0 = }(opposite)/(hypotenuse) \\ \\ \text{ Cos 0 = }(adjacent)/(Hypotenuse) \\ \\ \text{ Tan 0 = }(opposite)/(adjacent) \end{gathered}`

Step 2: Find the reciprocal of Sin 0?

`\begin{gathered} \text{ Reciprocal of Sin 0 = Cosec 0 = }\frac{1}{si\text{n 0}} \\ Recall,\text{ that Sin 0 = }\frac{opposite\text{ }}{Hypotenuse} \\ So,\text{ }\frac{1}{sin\text{ 0 }}\text{ = 1 }/\text{ }(opposite)/(Hypotenuse) \\ \\ \frac{1}{sin\text{ 0}}\text{ = Cosec 0 = 1 }*\text{ }(opposite)/(hypotenuse) \\ \text{ Cosec 0 = }\frac{1\text{ }*\text{ hypotenuse}}{opposite} \\ \text{ Cosec 0 = }(Hypotenuse)/(opposite) \end{gathered}`

Hence, Csc 0 is Hypotenuse / opposite

Option B