To solve for [tex]\( x \)[/tex] correct to one decimal place in the equation [tex]\( 7.1 \sin x = 0.798 \)[/tex], follow these steps:
1. Isolate [tex]\(\sin x\)[/tex]: First, divide both sides of the equation by 7.1:
[tex]\[
\sin x = \frac{0.798}{7.1}
\][/tex]
2. Calculate the ratio: Perform the division to find the value of [tex]\(\sin x\)[/tex]:
[tex]\[
\sin x = 0.1124
\][/tex]
3. Find the angle: To find [tex]\( x \)[/tex], take the inverse sine (arcsine) of 0.1124. This gives us [tex]\( x \)[/tex] in radians since standard scientific calculators and most programming libraries provide results in radians:
[tex]\[
x = \arcsin(0.1124)
\][/tex]
4. Convert to degrees (if needed): Often, it's practical to convert this result into degrees. The formula to convert from radians to degrees is:
[tex]\[
x_{\text{degrees}} = x_{\text{radians}} \times \frac{180}{\pi}
\][/tex]
5. Round the result: Finally, round both the radians and degrees results to one decimal place.
Using these steps, the results are:
- [tex]\(\sin x \approx 0.1124\)[/tex]
- [tex]\( x \approx 0.1 \)[/tex] radians
- [tex]\( x \approx 6.5 \)[/tex] degrees
Thus, when solving the equation [tex]\( 7.1 \sin x = 0.798 \)[/tex], [tex]\( x \approx 0.1 \)[/tex] radians or [tex]\( x \approx 6.5 \)[/tex] degrees to one decimal place.
