Sure! Let’s write a step-by-step solution to find [tex]\( x \)[/tex] by solving the trigonometric equation.
Given:
[tex]\[ x = \sin^{-1}(a) \][/tex]
Step-by-Step Solution:
1. Understand the equation: The equation [tex]\( x = \sin^{-1}(a) \)[/tex] means finding the angle [tex]\( x \)[/tex] whose sine is [tex]\( a \)[/tex].
2. Given [tex]\( a \)[/tex] value: We need to identify the value of [tex]\( a \)[/tex]. In our case, the value of [tex]\( a \)[/tex] is 0.5.
3. Rewrite the equation with the specific value: Replace [tex]\( a \)[/tex] in the equation with 0.5.
[tex]\[ x = \sin^{-1}(0.5) \][/tex]
4. Interpret the inverse sine function: The inverse sine function, [tex]\(\sin^{-1}(0.5)\)[/tex], will give us an angle [tex]\( x \)[/tex] such that [tex]\(\sin(x) = 0.5\)[/tex].
5. Find the value of [tex]\( x \)[/tex]: From the known trigonometric values, [tex]\(\sin(\frac{\pi}{6}) = 0.5\)[/tex]. Therefore, the angle whose sine is 0.5 is [tex]\(\frac{\pi}{6}\)[/tex] radians.
6. Numerical value: The numerical value of [tex]\(\frac{\pi}{6}\)[/tex] radians is approximately 0.5235987755982989.
Thus, the required value of [tex]\( x \)[/tex] is approximately [tex]\( 0.5235987755982989 \)[/tex] radians.
