Question

PLEASE HELP ME FIGURE THIS OUT 1..... WITH SCREENIES

Answer 1

Answer: sin $\frac{2\pi}{5}$

Step-by-step explanation:

The cofunction is the complement, which means their sum equals $\frac{\pi}{2}$ and the function switches. sin⇄cos, tan⇄cot, csc⇄sec.

cos $\frac{\pi}{10}$

$\frac{\pi}{2}$ - $\frac{\pi}{10}$

= $\frac{\pi}{2}(\frac{5}{5})$ - $\frac{\pi}{10}$

= $\frac{5\pi-\pi}{10}$

= $\frac{4\pi}{10}$

= $\frac{2\pi}{5}$

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csc θ = 6

csc = $\frac{hypotenuse}{opposite}$

• opposite = 1
• use Pythagorean Theorem to find adjacent = $\sqrt{35}$
• hypotenuse = 6

1² + (adjacent)² = 6²

      (adjacent)² = 35

      adjacent = $\sqrt{35}$

sin θ = $\frac{opposite}{hypotenuse}$ = $\frac{1}{6}$

cos θ = $\frac{adjacent}{hypotenuse}$ = $\frac{\sqrt{35}}{6}$

tan θ = $\frac{opposite}{adjacent}$ = $\frac{1}{\sqrt{35}}$ = $\frac{\sqrt{35}}{35}$

sec θ = $\frac{hypotenuse}{adjacent}$ = $\frac{6}{\sqrt{35}}$ = $\frac{6\sqrt{35}}{35}$

cot θ = $\frac{adjacent}{opposite}$ = $\frac{\sqrt{35}}{1}$ = $\sqrt{35}$