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Objective: Students will discover the six basic trigonometric functions. Ticket in: Fill in all of the RADIANS. 1 Objective: Students will discover the six basic trigonometric functions. Hypotenuse Opposite SOHCAHTOA θ Adjacent In your notes, write the three trigonometric ratios that are associated with SOHCAHTOA. sinθ= cosθ = tanθ = 2 Objective: Students will discover the six basic trigonometric functions. Hypotenuse Opposite SOHCAHTOA θ Adjacent If there are SIX trigonometric functions, what do you think the other ratios would be? 3 Objective: Students will discover the six basic trigonometric functions. These new ratios complete the six trigonometric functions. Match the new ratios with their "titles". Sine = sin θ O/H Cosecant = csc θ H/O Cosine = cos θ A/H Secant = sec θ H/A Tangent = tan θ O/A Cotangent = cot θ A/O What do you notice? 4 Objective: Students will discover the six basic trigonometric functions. 6 θ x 4 Find the missing side. Then, find the value of the six trigonometric functions of the angle θ. sin θ = csc θ = cos θ = sec θ = tan θ = cot θ = x = 5 Does this relate to the UNIT CIRCLE? sin θ = y cos θ = x tan θ = y/x (x, y) csc θ = 1/y sec θ = 1/x 1 y cot θ = x/y x (1, 0) 6 Look at the relationship between the functions. Which functions are reciprocals of each other? sin θ = y cos θ = x tan θ = y/x csc θ = 1/y (x, y) sec θ = 1/x 1 y x cot θ = x/y (1, 0) 7 H θ O There are three FUNDAMENTAL IDENTITIES for trig functions. A • Reciprocal Identities • Quotient Identities • Pythagorean Identities Today we will work with the first set of fundamental identities RECIPROCAL IDENTITIES 8 H θ O There are three FUNDAMENTAL IDENTITIES for trig functions. A • Reciprocal Identities 9 1 Given: sinθ = 4/5 and cosθ = 3/5 Find: secθ 10 2 Given: sinθ = 4/5 and cosθ = 3/5 Find: cscθ 11 3 Given: sinθ = 4/5 and cosθ = 3/5 Find: tanθ 12 4 Given: sinθ = 4/5 and cosθ = 3/5 Find: cotθ 13 Homework: • Do page 833 (8 - 19 all). Give exact answers only (fractions). Do not worry about decimal answers. 14