AboutPaul Klarreich Expertise I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction.
I can also try (but not guarantee) to answer questions on Abstract Algebra
-- groups, rings, etc. and Analysis -- sequences, limits, continuity.
I won't understand specialized engineering or business jargon.
Experience I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.
Expert: Paul Klarreich Date: 5/7/2008 Subject: Trigonometric identities
Question If x=acos0-bsin0 and y=asin0+bcos0, show that x^2+y^2=a^2+b^2 (0 equals the symbol theta).
Where should I start. Do I sub them in?
Answer Questioner: Patrick
Category: Advanced Math
Private: No
Subject: sin and cosine
Question: If x = a cos t - b sin t and
y = a sin t + b cost, show that x^2+y^2=a^2+b^2 (t equals the symbol theta).
Where should I start. Do I sub them in?
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Hi, Patrick,
Yes. (I suppose you want more than that.)
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Note: Since my recent difficulties I have been reducing my typing. I use a lot of abbreviations:
s = sin t
c = cos t
.................
Subst and then use the identity s^2 + c^2 = 1
(a c - b s)^2 + (a s + b c)^2 =
a^2 c^2 + b^2 s^2 - 2 ab sc + a^2 s^2 + b^2 c^2 + 2 ab sc =
a^2 c^2 + a^2 s^2 + b^2 s^2 + b^2 c^2 - 2 ab sc + 2 ab sc =
a^2 (c^2 + s^2) + b^2 (s^2 + c^2) - 2 ab sc + 2 ab sc =
