Answer: sin [tex]\frac{2\pi}{5}[/tex]
Step-by-step explanation:
The cofunction is the complement, which means their sum equals [tex]\frac{\pi}{2}[/tex] and the function switches. sin⇄cos, tan⇄cot, csc⇄sec.
cos [tex]\frac{\pi}{10}[/tex]
[tex]\frac{\pi}{2}[/tex] - [tex]\frac{\pi}{10}[/tex]
= [tex]\frac{\pi}{2}(\frac{5}{5})[/tex] - [tex]\frac{\pi}{10}[/tex]
= [tex]\frac{5\pi-\pi}{10}[/tex]
= [tex]\frac{4\pi}{10}[/tex]
= [tex]\frac{2\pi}{5}[/tex]
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csc θ = 6
csc = [tex]\frac{hypotenuse}{opposite}[/tex]
- opposite = 1
- use Pythagorean Theorem to find adjacent = [tex]\sqrt{35}[/tex]
- hypotenuse = 6
1² + (adjacent)² = 6²
(adjacent)² = 35
adjacent = [tex]\sqrt{35}[/tex]
sin θ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{1}{6}[/tex]
cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{\sqrt{35}}{6}[/tex]
tan θ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{1}{\sqrt{35}}[/tex] = [tex]\frac{\sqrt{35}}{35}[/tex]
sec θ = [tex]\frac{hypotenuse}{adjacent}[/tex] = [tex]\frac{6}{\sqrt{35}}[/tex] = [tex]\frac{6\sqrt{35}}{35}[/tex]
cot θ = [tex]\frac{adjacent}{opposite}[/tex] = [tex]\frac{\sqrt{35}}{1}[/tex] = [tex]\sqrt{35}[/tex]
