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Match the trigonometric functions with their values.

[tex]\[
\begin{array}{ll}
\text{Trigonometric Functions} & \text{Values} \\
\hline
\cos \frac{11 \pi}{6} & \square \\
\sin \frac{5 \pi}{6} & \square \\
\sin \frac{3 \pi}{4} & \square \\
\end{array}
\][/tex]

[tex]\[
\begin{array}{ll}
\frac{1}{2} & \longrightarrow \square \\
\frac{\sqrt{3}}{2} & \longrightarrow \square \\
\frac{\sqrt{2}}{2} & \longrightarrow \square \\
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
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]
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