Pre-Calculus Facts
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Tutorial 1 Very Useful (and Important) Trig Identities (i) sin 2 θ + cos 2 θ =1 (ii) tan 2 θ + 1 = sec 2 θ (iii) sin(2θ) = 2 sin θ cos θ (iv) cos(2θ) = cos 2 θ - sin 2 θ (v) sin(x + y) = sin x cos y + cos x sin y (vi) cos(x + y) = cos x cos y - sin x sin y There are also subtraction and multiplication identities! How To Find the Inverse of a One-to-One Function 1. Set y = f (x) 2. Solve the equation for x (i.e., write the equation as x = ... with its terms in y) 3. Interchange x and y, then you have y = f -1 (x). Rules of the Log Function (i) log b (xy) = log b (x) + log b (y) (ii) log b x y = log b (x) - log b (y) (iii) log b (x r )= r log b (x) (where r is any number in R) 1
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Useful Trig Identities and Log Rules
Transcript of Pre-Calculus Facts
Tutorial 1
Very Useful (and Important) Trig Identities
(i) sin2 θ + cos2 θ = 1
(ii) tan2 θ + 1 = sec2 θ
(iii) sin(2θ) = 2 sin θ cos θ
(iv) cos(2θ) = cos2 θ − sin2 θ
(v) sin(x+ y) = sinx cos y + cosx sin y
(vi) cos(x+ y) = cos x cos y − sinx sin y
There are also subtraction and multiplication identities!
How To Find the Inverse of a One-to-One Function
1. Set y = f(x)
2. Solve the equation for x (i.e., write the equation as x = ... with its terms in y)
3. Interchange x and y, then you have y = f−1(x).
Rules of the Log Function
(i) logb(xy) = logb(x) + logb(y)
(ii) logb
(x
y
)= logb(x)− logb(y)
(iii) logb (xr) = r logb(x) (where r is any number in R)
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