What is a positive value of A in the interval [ 0 ° , 90 ° ) \left[0\degree,90\degree\right) [ 0° , 90° ) that will make the following statement true? Express the answer in four decimal places. sin A = 0.9235 \sin A=0.9235 sin A = 0.9235

Let's give this problem a try. So here it says, what is a positive value of a in the interval from zero to 90 degrees that will make the following statement true? And we need to express our answer in four decimal places. Okay. So to solve this problem, all we really need to do is isolate a by itself. And we can do this by taking the inverse sign on both sides of this equation. This will get the inverse sign and the sign to cancel, leaving us with just a, which is what we're looking for. So a is going to equal the inverse sign of 0.9235. And if you go ahead and take this and plug it into your calculator, what you want to do is make sure your calculator is in degree mode. And we talked about how you can check this by pressing the mode button on your calculator, and you will should see a menu that says degree or radian. Make sure you are in degree mode. And the reason we want to be in degree mode is because, notice, our interval is from zero to 90 degrees. So that's a good sign that we need to use degree mode. So if you go ahead and plug this number into your calculator, the value that you should get is approximately 67.44324384, and then this keeps going on. But because we're asked to express our answer in four decimal places, looking at our decimal place, we need to go one, two, three, four places to the right of the decimal point, which will give us that a is equal to 67.4432 rounded to four decimal places. And that right there is the answer to the problem.

12. Trigonometric Functions

Trigonometric Functions on Right Triangles

Business Calculus

12. Trigonometric Functions

Trigonometric Functions on Right Triangles

Struggling with Business Calculus?

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Multiple Choice

What is a positive value of A in the interval $\left[0\degree,90\degree\right)$ that will make the following statement true? Express the answer in four decimal places.
$\sin A=0.9235$

$22.5568°$

$67.4432°$

$22.4432°$

$33.5438°$

Verified step by step guidance

Step 1: Recall the definition of the sine function. The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the hypotenuse. In this problem, we are solving for an angle A such that sin(A) = 0.9235.

Step 2: Use the inverse sine function (arcsin) to find the principal angle. The principal angle is the angle in the interval [0°, 90°) that satisfies the equation. Mathematically, this is written as A = arcsin(0.9235).

Step 3: Calculate the value of arcsin(0.9235) using a calculator or software. Ensure the calculator is set to degrees, as the problem specifies the interval in degrees.

Step 4: Verify that the calculated angle lies within the interval [0°, 90°). If it does not, adjust the angle accordingly to ensure it satisfies the given interval.

Step 5: Round the resulting angle to four decimal places, as specified in the problem. This will give the positive value of A that satisfies the equation sin(A) = 0.9235 within the interval [0°, 90°).