MATH 130 Sheet 4

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Dakota Wesleyan University
MATH 130 College Algebra and Trigonometry
Concepts addressed:
Apply the formulas for the trigonometric functions of x/2, 2x, x + y, and
trigonometric functions of x and y.
x – y in terms of the
Textbook: Algebra & Trigonometry, 4th Edition, by David Cohen, Brooks/Cole (ISBN 0-31406922-4)
Chapters to review for this concept:
9.1 – The Addition Formulas
9.2 – The Double-Angle Formulas
9.3 – The Product-to-Sum and Sum-to-Product Formulas
Know how to use and apply:
The Addition Formulas for Sine and Cosine:
sin(s + t) = sin s cos t + cos s sin t
sin(s – t) = sin s cos t – cos s sin t
cos(s + t) = cos s cos t – sin s sin t
cos(s – t) = cos s cos t + sin s sin t
The Addition Formulas for Tangent:
tan(s + t) = (tan s + tan t) / (1 – tan s tan t)
tan(s – t) = (tan s – tan t) / (1 + tan s tan t)
The Double-Angle Formulas:
sin2θ = 2 sinθ cosθ
cos 2θ = cos 2θ - sin 2θ
tan 2θ = 2 tanθ / (1 – tan 2θ)
The Half-Angle Formulas:
sin(s/2) = ± √ [(1 – cos s) / 2]
cos(s/2) = ± √ [(1 + cos s) / 2]
tan(s/2) = sin s / (1 + cos s)
Equivalent forms of the formula
Development of this review sheet was made possible by funding from the US Department of Education
through South Dakota’s EveryTeacher Teacher Quality Enhancement grant.
cos 2θ = cos 2θ - sin 2θ :
cos2θ = 2 cos 2θ – 1
cos2θ = 1 – 2 sin 2θ
cos 2θ = (1 + cos2θ) / 2
sin 2θ = (1 – cos2θ) / 2
The Product-to-Sum Formulas:
sinA sinB = ½ [cos(A – B) – cos(A + B)]
sinA cosB = ½ [sin(A – B) + sin(A + B)]
cosA cosB = ½ [cos(A – B) + cos(A + B)]
The Sum-to-Product Formulas:
sinA + sinB = 2 sin[(A+B)/2] cos[(A-B)/2]
sinA – sinB = 2 cos[(A+B)/2] sin[(A-B)/2]
cosA + cosB = 2 cos[(A+B)/2] cos[(A-B)/2]
cosA – cosB = -2 sin[(A+B)/2] sin[(A-B)/2]
Development of this review sheet was made possible by funding from the US Department of Education
through South Dakota’s EveryTeacher Teacher Quality Enhancement grant.
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