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Created with Fabric.js 1.4.5 ·We are learning to relate the six trigonometric to the unit circle·We are learning to understand how to solve real-life problems by using trigonometric ratios,properties of triangles of triangles, and the sine and cosine laws·We are learning to probe simple trigonometric identities George YeZhengGongGrate 11 Learning Goals: Performance Task ·I can use and apply the cosine, sine, tangent formulas·I can use the reciprocal identities, quotient identities and pythagorean identities·I can use and apply the cosine and sine laws Success Criteria: Trigonometric ratios for special angle The exact values of the primary trigonometric ratios for 30°, 45° and 60° anglescan be found by using the appropriate ratios of sides in isosceles right triangles and half-equilateral triangles with right angles.. if θ is acute angle in standard position, then·the terminal arm of the principal angle(180°- θ)lies in quadrant 2·the terminal arm of the principal angle(180°+ θ)lies in quadrant 3·the terminal arm of the principal angle(360°- θ)lies in quadrant 4 Trigonometric Ratios for Angles Greater than 90° ·In quadrant 1, All(A) ratios are positive because both x and y are positive.·In quadrant 2, only Sine(S) is positive, since x is negative and y is positive.·In quadrant 3, only Tangent(T) is positive because both x and y are negative.·In quadrant 4, only Cosine(C) is positive, since x is positive and y is negative. Trigonometric Ratios for Any Angle Between 0° and 360° Trigonometric Identities The Sine Law The sine law can be used if your know·Two sides and one angle opposite a given side(SSA) or ·Two angles and any side(AAS or ASA) The Cosine Law The cosine law can be used if you know·Two sides and the angle contained between those sides (SAS) or·All three sides(SSS) Solve problem by using·trigonometric ratios,·properties of triangles and·the sine and cosine laws
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