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 0 to 90 degrees that will make the following statement true, and we need to express our answer in 4 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 in 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 0 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 point 44324384, and then this keeps going on. But because we're asked to express our answer in 4 decimal places, looking at our decimal place, we need to go 1, 2, 3, 4 places to the right of the decimal point, which will give us that a is equal to 67.4 432 rounded to 4 decimal places. And that right there is the answer to the problem.

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0. Fundamental Concepts of Algebra3h 29m
1. Equations and Inequalities3h 27m
2. Graphs1h 43m
3. Functions & Graphs2h 17m
4. Polynomial Functions1h 54m
5. Rational Functions1h 23m
6. Exponential and Logarithmic Functions2h 28m
7. Measuring Angles40m
8. Trigonometric Functions on Right Triangles2h 5m
9. Unit Circle1h 19m
10. Graphing Trigonometric Functions1h 19m
11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
12. Trigonometric Identities 2h 34m
13. Non-Right Triangles1h 38m
14. Vectors2h 25m
15. Polar Equations2h 5m
16. Parametric Equations1h 6m
17. Graphing Complex Numbers1h 7m
18. Systems of Equations and Matrices3h 6m
19. Conic Sections2h 36m
20. Sequences, Series & Induction1h 15m
21. Combinatorics and Probability1h 45m
22. Limits & Continuity1h 49m
23. Intro to Derivatives & Area Under the Curve2h 9m

8. Trigonometric Functions on Right Triangles

Trigonometric Functions on Right Triangles

Precalculus

8. Trigonometric Functions on Right Triangles

Trigonometric Functions on Right Triangles

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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.
$\sin A=0.9235$

$22.5568°$

$67.4432°$

$22.4432°$

$33.5438°$

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Verified step by step guidance

Understand that the problem is asking for an angle A in the interval [0°, 90°) such that sin(A) = 0.9235.

Recall that the sine function is positive in the first quadrant, which is the interval [0°, 90°).

Use the inverse sine function, also known as arcsin, to find the angle A. This is done by calculating A = arcsin(0.9235).

Ensure that the calculator is set to degree mode since the problem specifies the angle in degrees.

After calculating, verify that the resulting angle is within the specified interval [0°, 90°) and round the answer to four decimal places.

6:4m

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Struggling with Precalculus?

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=0.9235sinA=0.9235

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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.
$\sin A=0.9235$