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Agenda – Fri. Dec. 9 (Day 1)

Agenda – Fri. Dec. 9 (Day 1). Note & Practice: Primary Trig Ratios Calculating the ratio Finding missing angle Finding missing side Today I will… “Start to learn about the trigonometry ratios of right angle triangles.”. Primary Trigonometry Ratios. The study of right angle triangles.

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Agenda – Fri. Dec. 9 (Day 1)

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  1. Agenda – Fri. Dec. 9 (Day 1) • Note & Practice: Primary Trig Ratios • Calculating the ratio • Finding missing angle • Finding missing side • Today I will… “Start to learn about the trigonometry ratios of right angle triangles.”

  2. Primary Trigonometry Ratios • The study of right angle triangles. • Angles in a triangle are related to the ratio of side lengths. Will this anglebe big or small? (compared to 45°) Will this anglebe big or small? (compared to 45°) Long Short Long Short

  3. Opposite and Adjacent • Angle θ • Angles are labeled with Greek letters such as:α, θ, etc. • Labeling Sides (for angle θ) • AB is the hypotenuse • BC is opposite to angle θ • AC is adjacent to angle θ B Hypotenuse Opposite θ A C Adjacent

  4. Opposite and Adjacent • Labeling Sides (for angle α) • AB is still the hypotenuse • AC is opposite to angle α • BC is adjacent to angle α B α Hypotenuse Adjacent A C Opposite

  5. Opposite and Adjacent • Opposite and adjacent depend on the angle under consideration. • The hypotenuse is always the same. B B Hypotenuse Opposite α Hypotenuse Adjacent θ A C Adjacent A C Opposite

  6. SOH CAH TOA • SOH • sine = opposite / hypotenuse • CAH • cosine = adjacent/ hypotenuse • TOA • tangent = opposite / adjacent

  7. Calculator Practice • To find the ratio given an angle • Use the “sin/cos/tan” button on your calculator • tan 25° = 0.4663 • sin 60° = • cos 43° = • To find an angle given theratio • Use the “sin-1/cos-1/tan-1” button on your calculator • tan-1(0.4663) = 25° • sin-1(0.7321) = • cos-1(0.2154) =

  8. Sine Ratio (sin θ) • Calculate the sine ratio: • sin θ = opposite / hypotenuse • sin θ = 5 / 13 • sin θ = 0.3846 • θ = sin-1(0.3846) • θ = 22.6° Opposite sin θ = Hypotenuse Hypotenuse 13 Opposite 5 θ A C

  9. Cosine Ratio (cosθ) • Calculate the cosine ratio: • cosθ = adjacent / hypotenuse • cosθ = 12 / 13 • cosθ = 0.9231 • θ = cos-1(0.9231) • θ = 22.6° Adjacent cosθ = Hypotenuse Hypotenuse 13 θ A C Adjacent 12

  10. Tangent Ratio (tan θ) • Calculate the tangent ratio: • tan θ = opposite / adjacent • tan θ = 5 / 12 • tan θ = 0.4167 • θ = tan-1(0.4167) • θ = 22.6° Opposite tan θ = Adjacent Opposite 5 θ A C Adjacent 12

  11. Find the Missing Side • Use the tangent ratio: • tan θ = opposite / adjacent • tan 30° = x / 12 • 0.5774 = x/12 • 12 (0.5774) = x • 6.9 = x Opposite tan θ = Adjacent Hypotenuse Opposite x 30° A C 12 Adjacent

  12. Find Another Missing Side • Use the cosine ratio: • cosθ = adjacent / hypotenuse • cos 20° = 10 / x • x cos 20° = 10 • x = cos 20° / 10 • x = 0.0940 Opposite cosθ = Adjacent Hypotenuse x Opposite 20° A C 10 Adjacent

  13. Homework • Pg. 362 #1-8alt • Pg. 372 #C1, 1-14,17-22

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