Answer :
Let's match the trigonometric functions to their corresponding values step-by-step:
1. Determine the values of the trigonometric functions:
- [tex]\( \cos \frac{11\pi}{6} \approx 0.87 \)[/tex]
- [tex]\( \sin \frac{5\pi}{6} \approx 0.5 \)[/tex]
- [tex]\( \sin \frac{3\pi}{4} \approx 0.71 \)[/tex]
2. Match these values with the given ones:
- [tex]\(0.5\)[/tex] matches with [tex]\( \sin \frac{5\pi}{6} \)[/tex]
- [tex]\(0.87\)[/tex] (which approximates [tex]\(\frac{\sqrt{3}}{2}\)[/tex]) matches with [tex]\( \cos \frac{11\pi}{6} \)[/tex]
- [tex]\(0.71\)[/tex] (which approximates [tex]\(\frac{\sqrt{2}}{2}\)[/tex]) matches with [tex]\( \sin \frac{3\pi}{4} \)[/tex]
So the correct pairs are:
[tex]\( \frac{\sqrt{3}}{2} \longrightarrow \cos \frac{11 \pi}{6} \)[/tex]
[tex]\( \frac{1}{2} \longrightarrow \sin \frac{5 \pi}{6} \)[/tex]
[tex]\( \frac{\sqrt{2}}{2} \longrightarrow \sin \frac{3 \pi}{4} \)[/tex]
1. Determine the values of the trigonometric functions:
- [tex]\( \cos \frac{11\pi}{6} \approx 0.87 \)[/tex]
- [tex]\( \sin \frac{5\pi}{6} \approx 0.5 \)[/tex]
- [tex]\( \sin \frac{3\pi}{4} \approx 0.71 \)[/tex]
2. Match these values with the given ones:
- [tex]\(0.5\)[/tex] matches with [tex]\( \sin \frac{5\pi}{6} \)[/tex]
- [tex]\(0.87\)[/tex] (which approximates [tex]\(\frac{\sqrt{3}}{2}\)[/tex]) matches with [tex]\( \cos \frac{11\pi}{6} \)[/tex]
- [tex]\(0.71\)[/tex] (which approximates [tex]\(\frac{\sqrt{2}}{2}\)[/tex]) matches with [tex]\( \sin \frac{3\pi}{4} \)[/tex]
So the correct pairs are:
[tex]\( \frac{\sqrt{3}}{2} \longrightarrow \cos \frac{11 \pi}{6} \)[/tex]
[tex]\( \frac{1}{2} \longrightarrow \sin \frac{5 \pi}{6} \)[/tex]
[tex]\( \frac{\sqrt{2}}{2} \longrightarrow \sin \frac{3 \pi}{4} \)[/tex]