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Lecture 10

MTH 162 Lecture 10: 6.2 Trigonometric Integrals and Substitutions Notes
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Department
Mathematics
Course
MTH 162
Professor
Pachero
Semester
Fall

Description
MTH 162 Calculus II 6.2 Trigonometric Integrals and Substitutions Notes L. Sterling Abstract Provide a generalization to each of the key terms listed in this section. Major Identities 2 2 sin (x2 + cos (x2 = 1 1 + tan (x) = sec (x) 1 + cot (x) = csc (x) sin(x + y) = sin(x)cos(y) + cos(x)sin(y) sin(x ▯ y) = sin(x)cos(y) ▯ cos(x)sin(y) sin(x ▯ y) = sin(x)cos(y) ▯ cos(x)sin(y) cos(x + y) = cos(x)cos(y) ▯ sin(x)sin(y) cos(x ▯ y) = cos(x)cos(y) + sin(x)sin(y) cos(x ▯ y) = cos(x)cos(y) ▯ sin(x)sin(y) Quotient and Reciprocal Identities Common Identities sin ▯ 1 1 sin ▯ = 1 = 1 = csc ▯ sin ▯ cos ▯ =cos ▯= 1 = 1 1 cos ▯ sec ▯ sin ▯ 1 1 tan ▯ = = cos ▯= cos ▯ sin ▯ cot ▯ csc ▯ = 1 sin ▯ 1 sec ▯ = cos ▯ cot ▯ = 1 tan ▯ Even-Odd Identities sin(▯x) = ▯sin(x) cos(▯x) = cos(x) tan(▯x) = ▯tan(x) 1 csc(▯x) = ▯csc(x) sec(▯x) = sec(x) cot(▯x) = ▯cot(x) Pythagorean Identities Common Identities First Pythagorean Identity and Its Equivalent Forms Pythagorean sin (x) + cos (x) = 1 Equivalent sin (x) = 1 ▯ cos (x) 2 2 cos (x) = 1 ▯ sin (x) Second Pythagorean Identity and Its Equivalent Forms Pythagorean 2 2 1 + cot (x) = csc (x) Equivalent 2 2 1 = csc (x) ▯ cot (x) sin (x) + cos (x) = csc (x) ▯ cot (x) 2 2 cot (x) = csc (x) ▯ 1 Third Pythagorean Identity and Its Equivalent Forms Pythagorean 1 + tan (x) = sec (x) Squared Identities Sine sin (▯) = 1 (1 ▯ cos(2▯)) = 1 ▯ cos(2▯) 2 2 Cosine 2 1 1 + cos(2▯) cos (▯) = (1 + cos(2▯)) = 2 2 Tangent 1▯cos(2▯) 2 sin ▯ 2 1 ▯ cos(2▯) tan (▯) = 2 = 1+cos(2▯)= cos ▯ 2 1 + cos(2▯)
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