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Understanding Trigonometric Ratios: Sine, Cosine, and Tangent Explained

Trigonometric ratios are essential for understanding the relationships between angles and sides in triangles. In this guide, we explore the three primary trigonometric ratios: sine (sin), cosine (cos), and tangent (tan). They are defined as follows: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = opposite/adjacent. Use the mnemonic SOHCAHTOA to easily remember these relationships. Practice calculating angles using trigonometric ratios, apply them to right triangles, and round your results to the nearest degree for accurate measurements.

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Understanding Trigonometric Ratios: Sine, Cosine, and Tangent Explained

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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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