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Trigonometric Addition & Subtraction Formula
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Trigonometric Addition & Subtraction Formula

by Zachary
(CA, USA)











































Use an Addition or Subtraction Formula to find the exact value of the expression

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May 05, 2012
Trigonometric Addition & Subtraction Formula
by: Staff


Question:

by Zachary
(Campbell CA, USA)


Use an Addition or Subtraction Formula to find the exact value of the expression




Answer:

tan (x + y) = [tan(x) + tan (y)] / [1 - tan(x) * tan(y)]

or

tan (x - y) = [tan(x) - tan (y)] / [1 + tan(x) * tan(y)]



tan (19π/12)

π/3 = 4π/12

tan (15π/12 + 4π/12)

tan (5π/4 + 4π/3)

tan (5π/4 + 4π/3) = [tan(5π/4) + tan (4π/3)] / [1 - tan(5π/4) * tan(4π/3)]

tan (5π/4 + 4π/3) = [tan(5π/4) + tan (4π/3)] / [1 - tan(5π/4) * tan(4π/3)]



tan(x) = sin(x) / cos(x)

tan(5π/4) = sin(5π/4) / cos(5π/4)

cos(5π/4) = -√(2)/2

sin(5π/4) = -√(2)/2

tan(5π/4) = -√(2)/2 / -√(2)/2

tan(5π/4) = 1


tan (4π/3) = sin(4π/3) / cos(4π/3)

sin(4π/3) = -√(3)/2

cos(4π/3) = -1/2

tan (4π/3) = [-√(3)/2] / [-1/2]

tan (4π/3) = √(3)


tan (19π/12) = [tan(5π/4) + tan (4π/3)] / [1 - tan(5π/4) * tan(4π/3)]


tan (19π/12) = [1 + √(3)] / [1 - 1* √(3)]


tan (19π/12) = -√(3) - 2

or

tan (19π/12) ≈ -3.7320508075689



>>> the final answer is (exact value):

tan (19π/12) = -√(3) – 2


>>> the final answer is (approximate value):

tan (19π/12) ≈ -3.7320508075689



Thanks for writing.

Staff
www.solving-math-problems.com



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