maths formulas/identities and trig derrivatives

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37 Terms

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derriviative of sin

cos

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derivative of cos

-sin

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integral of cos

sin x + c

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integral of sin

-cos x +c

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derrivative of -cosx

sin x

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integral of -cosx

-sinx + c

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derrivative of -sin x

-cos x

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integral of -sinx

cos x + c

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cosine rule

a2 =b2+c2- 2*b*c*cos(A)

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area of non right triangle

½absin(C)

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sec2x=

1+tan2(x)

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cosec2x=

1+cot2(x)

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arc length radians

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sector area radians

1/2r2θ

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range

all the y values

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domain

all the x values

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what transformation maps f(x) to f-1(x)

reflect in y=x

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formula for nth term of arithmetic sequence

un=a+(n-1)d

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nth term for geometric sequence

un=ar(n-1)

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derrivative of a^x (a is constant non e)

lna times a^x

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derriative of arcsin(x)

1/(1-x2)1/2

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derrivative of arccos(x)

-1/(1-x2)1/2

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derrivative of arctan(x)

1/(1+x2)

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how to find point of inflection

find second derivative check its 0 then check either side and if sign changes its inflection point.

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how to check if concave

if second derivative is negative when sub in x value its concave

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how to check if convex

if second derivative is positive when sub in x value its convex.

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factor theorem

(x-a) is a factor of f(x) IF f(a)=0

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how to find binomial p(x<n)

binomial cd with x value as n-1

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how to find binomial prob x less than or equal to n

x value = n this is default for calculator

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how to find binomial prob (x>n)

1-p(x</=n)

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how to find binomial P(x>/=n)

1-P(x</=n-1)

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simple random sampling

every member equally likely, assign each number and random number generate

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systemic sampling

take every k member from a population, e.g every 10th person

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stratified sampling

split into groups e.g gender then sample each group in proportion to size

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opportunity sampling

take whoever you can get until you have enough

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quota sampling

use opportunity sampling until you meet a set quota for each group e.g 10 women 10 men

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cluster

split population into clusters you expect to be similar then take sample from each cluster