Question

given sin a = .29 find the angle a in degrees. round your answer to the nearest hundredth. 16.86° 15.86° 14.86° 13.86°

Answer 1

Given that sin a = .29 then the angle a in degrees is 16.86

Answer 2

16.86°

Explanation:

Given the value for sin(a) = 0.29, we need to find the angle, in this case, a, whose sin(a) = 0.29.

In other words, we need to find the inverse function for the function in question.

In this case, the inverse function of sin(x) is arcsin(x) (which is also commonly known as
`\\ sin^(-1)(x)`).

So, for
`\\ sin(a) = 0.29`, we can find the function
`\\ sin^(-1)(x)` in a digital calculator, or asking WolframAlpha in Internet, so we have that
`\\ sin^(-1)(0.29)=16.86` degrees (°).

In fact, we can check this result for a = 16.86°:
`\\ sin(16.86) = 0.29`.

In other words, we found that 16.86° is the angle in degrees whose
`\\ sin(16.86) = 0.29`.

One word of caution: we need to be careful about if we are using degrees (known for this symbol ° ) or radians when calculating angles.

In the past, people were used to consult large tables with values for
`\\ sin(x), cos(x), tan(x)` and so on, and looking for the angle that generated such a value of
`\\ sin(x), cos(x), tan(x)`, respectively.

There are many other cases in which we have inverse functions, for example, logartithm is the inverse function of exponential function.