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Published byBlaze Lucas Modified over 6 years ago
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Warm Up Use trigonometric identities to simplify: csc ∙tan
cot ∙sin Find the value of in degrees (0°< < 90°) and radians (0< < π/2) w/o a calculator: csc = sec =
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4.4 Trig Functions of Any Angle
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Definitions of Trig Functions
Let be an angle in standard position with (x, y) a point on the terminal side of and Then… sin = y/r csc = r/y cos = x/r sec = r/x tan = y/x cot = x/y
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Check this Out… - cos tan + sin cos tan + sin - sin cos - sin tan +
II - cos tan + sin cos tan + sin - sin cos - sin tan + tan + cos IV III
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Example Let (4, -3) be a point on the terminal side of . Find the sin, cos and tan of . First we must find r. So r = Therefore: sin = -3/5 cos = 4/5 tan = -3/4
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EXAMPLE 2 Given cos = 3/5 and tan < 0, find sin and cot . Because the tan is negative and cos is positive, our answer is in quad___? x = 3 and r = 5, we need to find y. So… sin = -4/5 cot = -3/4
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Find the reference angle for the following angles
Reference Angles If is in standard position, then the reference angle ́ is the acute angle formed by the terminal side of and the x-axis. EXAMPLE Find the reference angle for the following angles = 125º = 5 = -135º
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More Examples… Evaluate each of the following: sin 210º cos (-5π/4)
tan (5π/3) Let be an angle in the third quadrant. Find: sin tan
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