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Geometry Lesson 9.5A Trigonometric Ratios Warm-Up: Ratios of Triangle Sides NEED A VOLUNTEER! Calculate the ratios in the table below Are the triangles similar? Why? What is true of the ratios in the table? Triangle Big Small a b c a c b c a b Trigonometric (“Trig”) Ratios Trig ratio: The ratio of the lengths of two sides of a right triangle There are three basic trig ratios: sine, cosine, and tangent These are abbreviated: Sine sin Cosine cos Tangent tan Sine, Cosine, Tangent The sine, cosine, and tangent of angle A are: A cos A = side adjacent A b hypotenuse c tan A = side opposite A a side adjacent A b c opposite sin A = side opposite A a hypotenuse c B adjacent b Notice that sin, cos, and tan operate on angles a C SOH-CAH-TOA! SOH: Sine is Opposite over Hypotenuse CAH: Cosine is Adjacent over Hypotenuse TOA: Tangent is Opposite over Adjacent Finding Trig Ratios Use the right triangles to find the specified trig ratios a sin A = c b b tan B = cos A = a c a sin J = tan A = b k b cos J = sin B = c l a tan J = cos B = c j l j k Finding Trig Ratios Find the sine, cosine, and tangent for each acute angle (round to 4 decimal places) 1. 2. 3. •sin F = 3/5 = 0.6 •cos F = 4/5 = 0.8 •tan F = 3/4 = 0.75 •sin D = 4/5 = 0.8 •cos D = 3/5 = 0.6 •tan D = 4/3 = 1.3333 •sin D = •cos D = •tan D = •sin F = •cos F = •tan F = •sin F = •cos F = •tan F = •sin D = •cos D = •tan D = Finding Trig Ratios Find the sine, cosine, and tangent for each acute angle (round to 4 decimal places) 4. 5. 6. •sin A = •cos A = •tan A = •sin N = •cos N = •tan N = •sin A = •cos A = •tan A = •sin C = •cos C = •tan C = •sin J = •cos J = •tan J = •sin E = •cos E = •tan E = Calculating Trig Ratios Using a scientific calculator or the trig table to find the following trig ratios (round to 4 decimal places): Angle sin cos tan Make sure calculator is in DEG mode TI-83, 84, etc. 1 SIN 0 Others: 1 0 SIN ENTER 10° 23° 30° 45° 60° 73° 89° 0.1736 0.3907 0.5000 0.7071 0.8660 0.9563 0.9998 0.9848 0.9205 0.8660 0.7071 0.5000 0.2924 0.0174 0.1763 0.4245 0.5774 1.0000 1.7321 3.2708 57.2900 sine and cosine: -1 to +1 tangent: – to + Closure Find the sine, cosine, and tangent of the acute angles of the special triangles below Write answers as radicals and approximations to 4 decimal places C 1 B C 45° 1 45° A B 60° 30° A Independent Practice A calculator with SIN, COS, and TAN functions will be useful! Ch 9.5 w/s