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How do you find the value of #cos ((3pi)/8)# using the double or half angle formula?

Answer 1

#(2 - sqrt2)/2#

Trig table, unit circle, and property of complementary arcs --> #cos ((3pi)/8) = cos (-pi/8 + (4pi/8)) = cos (-pi/8 + pi/2) =# #= sin (pi/8). # Find sin (pi/8) by using trig identity: #cos 2a = 1 - 2sin^2 a# #cos ((2pi)/8) = cos (pi/4) = sqrt2/2 = 1 - 2sin^2 (pi/8)# #2sin^2 (pi/8) = 1 - sqrt2/2 = (2 - sqrt2)/2# #sin^2 (pi/8) = (2 - sqrt2)/4# #sin (pi/8) = sqrt(2 - sqrt2)/2# (because #sin (pi/8)# is positive. Finally, #cos ((3pi)/8) = sin (pi/8) = sqrt(2 - sqrt2)/2#

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Answer 2

Charles Autterson

To find the value of cos((3π)/8) using the double or half angle formula, you can express (3π)/8 as a combination of known angles or multiples of known angles. In this case, you can rewrite (3π)/8 as (π/8) + (π/2). Then, you can use the half-angle formula for cosine, which states that cos(θ/2) = ±√((1 + cos(θ))/2). By substituting (π/8) + (π/2) for θ in the formula and simplifying, you can find the value of cos((3π)/8).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.