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Right Triangles and Trig Ratios SOH-CAH-TOA • SOH-CAH-TOA is an acronym used in Geometry and Right Triangle Trig to remember what sides of a right triangle go with which Trig Ratios • Each angle value (radians and degrees) has a specific ratio of sides that always holds true Consider an angle whose terminal ray passes through the point (4, 5) • In which quadrant does this angle fall? • Tell whether the sine, cosine and tangent are positive or negative for this angle (in Q1) Consider an angle whose terminal ray passes through the point (-4, 5) • In which quadrant does this angle fall? • Tell whether the sine, cosine and tangent are positive or negative for this angle (in Q2) Consider an angle whose terminal ray passes through the point (-4, -5) • In which quadrant does this angle fall? • Tell whether the sine, cosine and tangent are positive or negative for this angle (in Q3) Consider an angle whose terminal ray passes through the point (4, -5) • In which quadrant does this angle fall? • Tell whether the sine, cosine and tangent are positive or negative for this angle (in Q4) Trig Definitions/Ratios • Since the opposite always refers to the vertical distance and the adjacent always refers to the horizontal distance, we can say that… y sin r x cos r y tan x Sign Analysis Chart Examples • Tell whether each of the following is positive or negative: sin 240 Examples • Tell whether each of the following is positive or negative: sin 240 cos 300 Examples • Tell whether each of the following is positive or negative: sin 240 3 tan 4 cos 300 Examples • Tell whether each of the following is positive or negative: sin 240 cos 300 3 tan 4 4 sin 3 Finding Exact Values • If is a quadrant angle find sin and cos 4th 5 and tan 12 , Finding Exact Values • An angle has a terminal ray that passes through the point (-4, 7). Find the exact value of the three trig ratios in simplest form. The Unit Circle (Quadrantal Angles) • Consider a circle with radius = ____ – What is the sin 90? – Does the size of the circle matter when evaluating the trig ratios? The Unit Circle (Quadrantal Angles) Examples • Find the exact value for each of the following: sin 270 Examples • Find the exact value for each of the following: sin 270 tan 90 Examples • Find the exact value for each of the following: sin 270 cos tan 90 Examples • Find the exact value for each of the following: sin 270 tan 90 cos 5 sin 2 Homework • Pg. 272 (1 – 27odd)