Question Video: Solving an Equation Using the Inverse Sine Function Mathematics

Find the acute angle 𝑥° that satisfies sin (𝑥 + 2) = 0.2. Round your answer to two decimal places.

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Video Transcript

Find the acute angle 𝑥 degrees that satisfies sin of 𝑥 plus two is equal to 0.2. Round your answer to two decimal places.

In this question, we are told that 𝑥 is an acute angle. And since it is measured in degrees, it must be greater than zero and less than 90. We need to calculate the value of 𝑥 by solving the equation sin of 𝑥 plus two equals 0.2. We will begin by recalling the properties of inverse trigonometric functions. We know that if the angle 𝜃 lies between negative 90 and 90 degrees, then the inverse sin of sin 𝜃 equals 𝜃. Since 𝑥 is an acute angle, this means that we can take the inverse sine of both sides of our equation, giving us 𝑥 plus two is equal to inverse sin of 0.2.

Ensuring that our calculator is in degree mode, we can type the right-hand side into the calculator. This gives us 11.5369 and so on. As this is equal to 𝑥 plus two, we can subtract two from both sides of this equation to calculate 𝑥. 𝑥 is therefore equal to 9.5369 and so on. We are asked to round our answer to two decimal places. And since the third digit after the decimal point is a six, we will round up. The acute angle 9.54 degrees satisfies the equation sin of 𝑥 plus two is equal to 0.2 to two decimal places.

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