Purdue MA 15400 - Trigonometric Functions of Angles - D1429880

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Purdue MA 15400 - Trigonometric Functions of Angles

School name Purdue University

Course Ma 15400- Algebra and Trigonometry II

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MA 154 Lesson 3 DelworthMA 154 Lesson 3 DelworthSection 6.2 Trigonometric Functions of AnglesThe Fundamental Identities:(1) The reciprocal identities:csc1sinsec1coscot1tan(2) The tangent and cotangent identities:tansincoscotcossin(3) The Pythagorean identities:sin2 cos21 1 tan2sec21 cot2csc2Take the simple right triangle with sides 3, 4 and 5 with  opposite the side of length 4.Find sin and cos, now find sin2 cos2sin2 cos21 is a Pythagorean identity since it is derived from the Pythagorean Theorem.Divide both sides by sin2to find another Pythagorean identity.Divide both sides by cos2to find yet another one.Each of the three Pythagorean identities creates two more identities by subtracting a term from the left side to the right side. sin2 cos21 1 tan2sec21 cot2csc2sin21 cos2tan2sec2 1 cot2csc2 1cos21 sin21sec2 tan21csc2 cot2Verify the identity by transforming the left side into the right side.tancot1sin 3 cot 3 cos 3 1MA 154 Lesson 3 DelworthSection 6.2 Trigonometric Functions of Anglessectancscsin2 cos2sin21 cot2(1 cos)(1 cos) sin2cos2sec2 1 sin21 sin2 1 tan2 1cot tancscsec 2MA 154 Lesson 3 DelworthSection 6.2 Trigonometric Functions of AnglesUsing the coordinate system, Notice that the adjacent side corresponds to the x-value of the coordinate and the opposite side corresponds the y-value of the coordinateThe idea that the cosine of  corresponds to the x-axis and the sine of  corresponds to the y-axis is one that you need to get use to.If  is an angle in standard position on a rectangular coordinate system and if P(-5, 12) is on theterminal side of , find the values of the six trigonometric functions of .If  is an angle in standard position on a rectangular coordinate system and if P(4, 3) is on the terminal side of , find the values of the six trigonometric functions of .Find the exact values of the six trigonometric functions of  if  is in standard position and the terminal side of  is in the specified quadrant and satisfies the given condition.III; on the line 4x – 3y = 0 II; parallel to the line 3x + y – 7 = 03(x, y)MA 154 Lesson 3 DelworthSection 6.2 Trigonometric Functions of AnglesFind the quadrant containing  if the given conditions are true.a) tan  < 0 and cos  > 0b) sec  > 0 and tan  < 0c) csc  > 0 and cot  < 0d) cos  < 0 and csc  < 0Use the fundamental identities to find the values of the trigonometric functions for the given conditions:tan125 and cos 0sec 4 and csc 0

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