Henry is asked to find the exact value of \([tex]$\cos \frac{10 \pi}{3}$\)[/tex]. His steps are shown below.
1. Subtract \([tex]$2 \pi$\)[/tex] from \([tex]$\frac{10 \pi}{3}$\)[/tex] as many times as possible:
\([tex]$
\frac{10 \pi}{3}-2 \pi=\frac{4 \pi}{3}
$\)[/tex]
2. Find the reference angle for \([tex]$\frac{4 \pi}{3}: \frac{3 \pi}{2}-\frac{4 \pi}{3}=\frac{\pi}{6}$\)[/tex] :
3. The cosine value for \([tex]$\frac{\pi}{6}$\)[/tex] is \([tex]$\frac{\sqrt{3}}{2}$\)[/tex].
4. The cosine value is positive because \([tex]$\frac{\pi}{6}$\)[/tex] is in the first quadrant.
Which of the following describes Henry's errors?
1. Subtract \([tex]$2 \pi$\)[/tex] from \([tex]$\frac{10 \pi}{3}$\)[/tex] as many times as possible:
\([tex]$
\frac{10 \pi}{3}-2 \pi=\frac{4 \pi}{3}
$\)[/tex]
2. Find the reference angle for \([tex]$\frac{4 \pi}{3}: \frac{3 \pi}{2}-\frac{4 \pi}{3}=\frac{\pi}{6}$\)[/tex] :
3. The cosine value for \([tex]$\frac{\pi}{6}$\)[/tex] is \([tex]$\frac{\sqrt{3}}{2}$\)[/tex].
4. The cosine value is positive because \([tex]$\frac{\pi}{6}$\)[/tex] is in the first quadrant.
Which of the following describes Henry's errors?