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Trigonometric Ratios

Trigonometric Ratios. A RATIO is a comparison of two numbers. For example; boys to girls cats : dogs right : wrong. In Trigonometry, the comparison is between sides of a triangle. Trig. Ratios. Θ this is the symbol for an unknown angle measure. It’s name is ‘Theta’.

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Trigonometric Ratios

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  1. Trigonometric Ratios A RATIO is a comparison of two numbers. For example; boys to girls cats : dogs right : wrong. In Trigonometry, the comparison is between sides of a triangle.

  2. Trig. Ratios

  3. Θ this is the symbol for an unknown angle measure. It’s name is ‘Theta’. Easy way to remember trig ratios: SOH CAH TOA Three Trigonometric Ratios • Sine – abbreviated ‘sin’. • Ratio: sin θ = opposite side hypotenuse • Cosine - abbreviated ‘cos’. • Ratio: cos θ = adjacent side hypotenuse • Tangent - abbreviated ‘tan’. • Ratio: tan θ = opposite side adjacent side

  4. Let’s practice… Write the ratio for sin A Sin A = a c Write the ratio for cos A Cos A = b c Write the ratio for tan A Tan A = a b B c a C b A Let’s switch angles: Find the sin, cos and tan for Angle B: Tan B = b a Sin B = b c Cos B = a c

  5. Make sure you have a calculator… Set your calculator to ‘Degree’….. MODE (next to 2nd button) Degree (third line down… highlight it) 2nd Quit

  6. Let’s practice… Find an angle that has a tangent (ratio) of 2 3 Round your answer to the nearest degree. C 2cm B 3cm A Process: I want to find an ANGLE I was given the sides (ratio) Tangent is opp adj TAN-1(2/3) = 34°

  7. 8 A 4 Practice some more… Find tan A: 24.19 12 A 21 Tan A = opp/adj = 12/21 Tan A = .5714 Find tan A: 8 Tan A = 8/4 = 2

  8. Trigonometric Ratios • When do we use them? • On right triangles that are NOT 45-45-90 or 30-60-90 Find: tan 45 1 Why? tan = opp hyp

  9. Your assignment Pg 336: 22 - 33 Pg 635: 12 - 17

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