Finding the angle from sin(2 theta)=0.348

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In summary, to find the second angle in this problem, we can use the property of (2 theta) and set it equal to x. This gives us two possible values for x, 20.4 and 180-20.4. By substituting x back in terms of θ, we can solve for the second angle.
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maiad
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I was wonder how to find the second angle to this problem. I already know one of the angle is 10.2 degree but shouldn't the the second angle be 180-(2*10.2) since in the second quadrant, sin values are positive but in the book, it's given as 90-10.2. Is it something to do with the properties of (2 theta)?
 
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maiad said:
I was wonder how to find the second angle to this problem. I already know one of the angle is 10.2 degree but shouldn't the the second angle be 180-(2*10.2) since in the second quadrant, sin values are positive but in the book, it's given as 90-10.2. Is it something to do with the properties of (2 theta)?
Let x=2θ. Then you have sin x = 0.348, so x=20.4 or x=180-20.4. Now write x in terms of θ and solve.
 
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1. What is the value of theta?

The value of theta cannot be determined solely from the given equation. Sin(2 theta) is equal to 0.348, but this does not provide enough information to find the value of theta. More information or equations are needed.

2. How do you find the angle from a sine value?

To find the angle from a sine value, you need to use the inverse sine function or arcsine. The arcsine of a number is the angle whose sine is that number. In this case, you would use the arcsine of 0.348 to find the angle.

3. Can you solve for theta without a calculator?

No, solving for theta from a sine value requires the use of a calculator or a mathematical software program. The inverse sine function is not easily solved by hand.

4. Is there only one solution for theta?

No, there are multiple solutions for theta when given a sine value. The inverse sine function has an infinite number of solutions because sine is a periodic function. This means that there are multiple angles that have the same sine value.

5. Can you use other trigonometric functions to find theta?

Yes, you can use other trigonometric functions such as cosine or tangent to find the angle theta. However, you would need more information or equations to determine the specific value of theta.

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