(All Trigonometry Formula)

$$ {J(\theta) =\frac{1}{2m} [\sum^m_{i=1}(h_\theta(x^{(i)}) - y^{(i)})2 + \lambda\sum^n_{j=1}\theta^2_j} $$

\(sinx+siny=2sin\frac{x+y}{2}cos\frac{x-y}{2}\)

\(x^2 = \sqrt{y}\)

\(sin(90°-x)=\cosx

Trigonometry formula

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Trigonometry formulas are used to solve problems based on the sides and angles of a right-angled triangle, using the different trigonometric identities. These formulas can be used to evaluate trigonometric ratios(also referred to as trigonometric functions), sin, cos, tan, csc, sec, and cot.

Trigonometrical Ratios

1. \(sin(θ)=\frac{p}{h}\)
2. \(cos(θ)=\frac{b}{h}\)
3. \(tan(θ)=\frac{p}{b}\)
4. \(cot(θ)=\frac{b}{p}\)
5. \(sec(θ)=\frac{h}{b}\)
6. cosec_=h/p

All trigonometry formula

1. \(sin(90°-θ)=\cosθ\)
2. \(cos(90°-θ)=\sinθ\)
3. \(tan(90°-θ)=\cotθ\)
4. \(cot(90°-θ)=\tanθ\)
5. \(sec(90°-θ)=cosecθ\)
6. \(cosec(90°-θ)=\secθ\)

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1. \(sin(90°+θ)=cosθ\)
2. \(cos(90°+θ)=-\sinθ\)
3. \(tan(90°+θ)=-\cotθ\)
4. \(cot(90°+θ)=-\tanθ\)
5. \(sec(90°+θ)=-cosecθ\)
6. \(cosec(90°+θ)=secθ\)

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1. \(sin(180°-θ)=sinθ\)
2. \(cos(180°-θ)=-\cosθ\)
3. \(tan(180°-θ)=-\tanθ\)
4. \(cot(180°-θ)=-\cotθ\)
5. \(sec(180°-θ)=-\secθ\)
6. \(cosec(180°-θ)=cosecθ\)

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1. \(sin(90°-)=\cosθ\)
2. \(cos(90°-θ)=\sinθ\)
3. \(tan(90°-θ)=\cotθ\)
4. \(cot(90°-θ)=\tanθ\)
5. \(sec(90°-θ)=cosecθ\)
6. \(cosec(90°-θ)=secθ\)

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1. \(sin(A+B)=sinA.cosB+cosA.sinB\)
2. \(sin(A-B)=sinA.cosB-cosA.sinB\)
3. \(cos(A+B)=cosA.cosB-sinA.sinB\)
4. \(cos(A-B)=cosA.cosB+sinA.sinB\)
5. \(tan(A+B)=\frac{tanA+tanB}{1-tanA.tanB}\)
6. \(tan(A-B)=\frac{tanA-tanB}{1+tanA.tanB}\)
7. \(cot(A+B)=\frac{cotA.cotB-1}{cotB+cotA}\)
8. \(cot(A-B)=\frac{cotA.cotB+1}{cotB-cotA}\)

\(θ=\)	sin	cos	tan	cot	sec	cosec
\(0°\)	\(0\)	\(1\)	\(0\)	\(∞\)	\(1\)	\(∞\)
\(30°\)	\(\frac{1}{2}\)	\(\frac{\sqrt{3}}{2}\)	\(\frac{1}{\sqrt{3}}\)	\(\sqrt{3}\)	\(\frac{2}{\sqrt{3}}\)	\(2\)
\(45°\)	\(\frac{1}{\sqrt{2}}\)	\(\frac{1}{\sqrt{2}}\)	\(1\)	\(1\)	\(\sqrt{2}\)	\(\sqrt{2}\)
\(60°\)	\(\frac{\sqrt{3}}{2}\)	\(\frac{1}{2}\)	\(\sqrt{3}\)	\(\frac{1}{\sqrt{3}}\)	\(2\)	\(\frac{2}{\sqrt{3}}\)
\(90°\)	\(1\)	\(0\)	\(∞\)	\(0\)	\(∞\)	\(1\)
\(120°\)	\(\frac{\sqrt{3}}{2}\)	\(-\frac{1}{2}\)	\(-\sqrt{3}\)	\(-\frac{1}{\sqrt{3}}\)	\(-2\)	\(\frac{2}{\sqrt{3}}\)
\(135°\)	\(\frac{1}{\sqrt{2}}\)	\(-\frac{1}{\sqrt{2}}\)	\(1\)	\(-1\)	\(\sqrt{2}\)	\(\sqrt{2}\)
\(150°\)	\(\frac{1}{2}\)	\(-\frac{\sqrt{3}}{2}\)	\(-\frac{1}{\sqrt{3}}\)	\(-\sqrt{3}\)	\(\frac{2}{\sqrt{3}}\)	\(2\)
\(180°\)	\(0\)	\(-1\)	\(0\)	\(∞\)	\(-1\)	\(∞\)

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