HOMEWORK 12
(1) (?) Prove the angle-addition formulæ sin(α+β) = sin(α) cos(β)+cos(α) sin(β)
and cos(α + β) = cos(α) cos(β) − sin(α) sin(β), at least for 0 < α, β, α + β <
π/2. (Hint: The trigonometric functions can be defined in terms of the unit
circle, or of right triangles. You will probably want to pick one definition
and deduce its consequences.)
= 1.
(2) We showed in class that limh→0+ sin(h)
h
(a) Prove that limh→0− sin(h)
=
1
as
well.
h
(b) (?) Compute limh→0 cos(h)−1
. (Hint: Multiply the numerator and
h
denominator by an appropriately chosen factor.)
(3) Compute sin0 (x) and cos0 (x). (Hint: The correct answer here is not just a
formula, but rather a proof that that formula is correct. Use the previous
problems.)
Date:
Last updated: 7 April 2010
Due: 13 April 2010.
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