Operator notations -Trigonometry formulas

Operator notations Gradient: In the three-dimensional Cartesian coordinate variables, the gradient of some function f(x,y,z) is given by: grad(f)=∇f=(∂∂x,∂∂y,∂∂z)f=∂f∂xi+∂f∂yj+∂f∂zk where i, j, k are the standard unit vectors for the…

Continue Reading Operator notations -Trigonometry formulas

Negative angle identities -Trigonometry formulas

Negative angle identities 1. sin(−t)=−sin(t) 2. cos(−t)=cos(t) 3. tan(−t)=−tan(t) 4. cot(−t)=−cot(t) 5. sec(−t)=sec(t) 6. cosec(−t)=−cosec(t) Example 1: What is $$\cos \left(-\frac {3\pi }{4}\right)$$? Solution: cos-3π4=cos3π4=-22 Example 2: What is $$\sin \left(-\frac {\pi }{2}\right)$$? Solution:…

Continue Reading Negative angle identities -Trigonometry formulas

Allied angles table -Trigonometry formulas

Allied angles table $$\alpha$$ $$\sin \alpha$$ $$\cos \alpha$$ $$\tan \alpha$$ $$\cot \alpha$$ $$\sec \alpha$$ $$\text{cosec} \alpha$$ $$-\theta$$ $$-\sin \theta$$ $$+\cos \theta$$ $$-\tan \theta$$ $$-\cot \theta$$ $$+\sec \theta$$ $$-\text{cosec} \theta$$…

Continue Reading Allied angles table -Trigonometry formulas

Euler's formula $$1. \ \sin \theta = \frac {1}{2i} \left( e^{i \theta } - e^{-i \theta } \right)$$ $$2. \ \cos \theta = \frac {1}{2} \left( e^{i… Continue Reading Euler’s formula -Trigonometry formulas Powers of functions -Trigonometry formulas Powers of functions$$ 1. \ \sin^2 α= \frac {(1 − \cos 2α)}{2}  2. \ \sin^3 α= \frac {(3 \sin α – \sin 3α)}{4}  3. \…

Continue Reading Powers of functions -Trigonometry formulas

Product-to-Sum Identities

Product-to-Sum Identities 1. sinα·sinβ=12cos(α–β)–cos(α+β) 2. cosα·cosβ=12cos(α–β)+cos(α+β) 3. sinα·cosβ=12sin(α+β)+sin(α–β) 4. cosα·sinβ=12sin(α+β)–sin(α–β) 5. tanα·tanβ=(tanα+tanβ)(cotα+cotβ) 6. cotα·cotβ=(cotα+cotβ)(tanα+tanβ) 7. tanα·cotβ=(tanα+cotβ)(cotα+tanβ) Example: Write cos 3x cos 2x as a sum Solution: cosα·cosβ=12[cos(α–β)+cos(α+β)] cos3x·cos2x=12[cos(3x–2x)+cos(3x+2x)] cos3x·cos2x=12[cosx+cos5x] cos3x·cos2x=cosx2+cos5x2

Sum-to-Product Identities

Sum-to-Product Identities 1. Sum of sines sinα+sinβ=2sinα+β2cosα-β2 \sin \alpha + \sin \beta = 2 \sin \frac {\alpha + \beta}{2} \cos \frac {\alpha - \beta}{2} 2. Difference of sines sinα-sinβ=2cosα+β2sinα-β2 \sin…

Half/Double/Multiple angle formula

Half/Double/Multiple angle formula Half angle formula: $$1.\ \sin \frac A2 = \pm \sqrt \frac{(1- \cos A)}{2}$$ $$2.\ \cos \frac A2 = \pm \sqrt \frac{(1+ \cos A)}{2}$$…