$\sin 30^{\circ}=0.5$

Using the equality above, copy and complete the following:
$\sin ^{-1}(0.5)=$

The problem states that sin 3 0 ∘ = 0.5 .
We need to find the value of sin − 1 ( 0.5 ) .
Since sin 3 0 ∘ = 0.5 , then sin − 1 ( 0.5 ) = 3 0 ∘ .
Therefore, sin − 1 ( 0.5 ) = 3 0 ∘ ​ .

Explanation

Understanding the problem We are given that sin 3 0 ∘ = 0.5 . The problem asks us to find the value of sin − 1 ( 0.5 ) . The inverse sine function, denoted as sin − 1 ( x ) , gives the angle whose sine is x . In other words, if sin ( y ) = x , then sin − 1 ( x ) = y .

Applying the inverse sine function Since sin 3 0 ∘ = 0.5 , it follows that sin − 1 ( 0.5 ) = 3 0 ∘ .

Final Answer Therefore, the answer is 3 0 ∘ .


Examples
Imagine you are designing a ramp for a skateboard park. You want the ramp to have an angle such that for every 1 unit of vertical height, the ramp extends 2 units horizontally. This means the sine of the angle of the ramp should be 1/2 = 0.5. Using the inverse sine function, you can calculate the exact angle needed: sin − 1 ( 0.5 ) = 3 0 ∘ . This ensures your ramp has the desired slope for skateboarders to perform their tricks safely.

Answered by GinnyAnswer | 2025-07-08