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Home/Tag: Trig Functions
5 11, 2016

## Trig Identities

Trig Identities sin2 x + cos2 x = 1 worked examples further examples Solve 2cos2 x – sin x – 1 = 0 for –π ≤ x ≤ π. cos2 x = 1 - sin2 x 2(1 - sin2 x) - sin x - 1 = 0 2 - 2 sin2 [...]

5 11, 2016

## Arc Length

Arc Length $L=\theta\;r$ worked examples further examples harder examples a. $8\pi=\frac{2\pi}{3}\times\;r$ $24\pi=2\pi\;r$ r = 12 units b. segment XPY A = ½ r2(θ - sin θ) A = ½ × (12√3)2($\pi$/3 - sin $\pi$/3) A = 216($\pi$/3 - √3/2) u2 A = [...]

3 08, 2016

## Trig Maxima/Minima

Trig Maxima/Minima worked examples further examples harder examples trig functions maxima/minima forum

25 07, 2016

## Trig Tangents & Normals

Trig Tangents & Normals $y=\sin x$ $\frac{dy}{dx}=\cos x$ $y=\cos x$ $\frac{dy}{dx}=-\sin x$ $y=\tan x$ $\frac{dy}{dx}=\sec^2 x$ worked examples Find the equation of the tangent to y = 2sin 2x – 3 at the point where x = 0.  y' = [...]

12 08, 2015

## Exam Style Questions

Exam Style Questions In the diagram P and Q are two points on the parabola y = 1 - x2. The tangents to the parabola at P and Q intersect each other on the y-axis at A and the x-axis at B and C respectively. Triangle ABC is an [...]

12 08, 2015

## Trig Graphs & Equations

Trig Graphs & Equations y = sin x Period = $2\pi$ Amplitude = 1 y = cos x Period = $2\pi$ Amplitude = 1 y = tan x Period = $\pi$ worked examples Solve the trigonometric equation cos x = ½, for 0 [...]

12 08, 2015

## Period & Frequency

Period & Frequency Period Period = $\frac{2\pi}{n}$ for y = sin (nx) and cos (nx) Period Period = $\frac{\pi}{n}$ for y = tan (nx)  Frequency $f=\frac1T$ worked examples

12 08, 2015

## Trig Graphs

Trig Graphs y = sin x Period = 2$\pi$ Amplitude = 1 y = cos x Period = 2$\pi$ Amplitude = 1 y = tan x Period = $\pi$ worked examples Draw the graph of y = 3sin 2x for 0 ≤ x ≤ [...]

12 08, 2015

## Simpson’s Rule

Simpson's Rule h/3{f(a) + f(b) + 4(sum of odds) + 2(sum of evens)} worked examples The length of one arch of the curve y = sin x is given by $\int\limits_0^{\pi } {\sqrt{1+\cos^2\,x}\;dx}$. Find the approximate length using Simpson's rule with three function values. $0,\;\frac{\pi}{2},\;\pi$ find the three [...]

12 08, 2015

## Trig Volumes

Trig Volumes $\int sin\;x\; dx = -cos\; x\; + c$ $\int cos\; x\; dx =sin\; x\; + c$ $\int\sec^2 x\; dx =tan\; x\; + c$ worked examples Find the volume generated when the curve $y = \sqrt {\cot \;x}$is rotated about the [...]