Video Transcript
Fill in the blank: Given that 𝑥 is an acute angle, if sin 𝑥 is equal to 𝑎 and 𝑎 is greater than negative one and less than one, then 𝑥 is equal to what.
In this question, we are given an equation sin 𝑥 is equal to 𝑎, where 𝑥 is an acute angle. This means that 𝑥 lies between zero and 90 degrees, or if our angle is measured in radians between zero and 𝜋 over two radians. We are also told that the value of 𝑎 lies between negative one and one. This is important since sin 𝑥 is only valid between these values. We can recall this by studying the sine graph between zero and 90 degrees.
To find an expression for 𝑥, we begin by considering the equation sin 𝑥 equals 𝑎. We can take the inverse sine or arcsine of both sides of this equation. And we recall that the inverse sin of sin 𝜃 is simply equal to 𝜃. This means that the inverse sin of sin 𝑥 is 𝑥. And this is equal to the inverse sin of 𝑎.
If 𝑥 is an acute angle and if sin 𝑥 is equal to 𝑎, where 𝑎 is greater than negative one and less than one, then 𝑥 is equal to the inverse sin or arcsin of 𝑎.