Answer:
16.86°
Step-by-step 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.
