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The terminal side of an angle θ in standard position intersects the unit circle at (\frac{\sqrt{2}}{2},...

The terminal side of an angle θ in standard position intersects the unit circle at (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})
Find sin(θ), cos(θ), and tan(θ).
The terminal side of an angle θ in standard position intersects the unit circle at (\frac{1}{2}, \frac{\sqrt{3}}{2})
Find sin(θ), cos(θ), and tan(θ).
The terminal side of an angle θ in standard position in Quadrant I intersects the unit circle at (x, \frac{8}{17})
a. Find the missing coordinate.
b. Find sin(θ).
c. Find cos(θ).
d. Find tan(θ).
The terminal side of an angle θ in standard position in Quadrant I intersects the unit circle at (\frac{\sqrt{5}}{3}, y)
Find tan(θ).
Use the unit circle to find sin(\frac{\pi}{6}), cos(\frac{\pi}{6}), tan(\frac{\pi}{6})
Use the unit circle to find sin(\frac{\pi}{3}), cos(\frac{\pi}{3}), tan(\frac{\pi}{3})

Answer

  1. sin(θ) = \(\frac{\sqrt{2}}{2}\), cos(θ) = \(\frac{\sqrt{2}}{2}\), tan(θ) = 1

  2. sin(θ) = \(\frac{\sqrt{3}}{2}\), cos(θ) = \(\frac{1}{2}\), tan(θ) = \(\sqrt{3}\)

    1. x = \(\frac{15}{17}\)

    2. sin(θ) = \(\frac{8}{17}\)

    3. cos(θ) = \(\frac{15}{17}\)

    4. tan(θ) = \(\frac{8}{15}\)

  3. y = \(\frac{2}{3}\), tan(θ) = \(\frac{2}{\sqrt{5}}\)

  4. sin(\frac{\pi}{6}) = \(\frac{1}{2}\), cos(\frac{\pi}{6}) = \(\frac{\sqrt{3}}{2}\), tan(\frac{\pi}{6}) = \(\frac{1}{\sqrt{3}}\)

  5. sin(\frac{\pi}{3}) = \(\frac{\sqrt{3}}{2}\), cos(\frac{\pi}{3}) = \(\frac{1}{2}\), tan(\frac{\pi}{3}) = \(\sqrt{3}\)

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