Trigonometric Identities

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Odd

cot(−θ)

-cot θ

Odd

tan (-θ)

-tan θ

Odd

csc (-θ)

-csc θ

Odd

sin (-θ)

-sin θ

Even

cos (-θ)

cos θ

Even

sec (-θ)

sec θ

Cofunction

tan ($\frac{\pi}{2}$ - θ)

cot θ

Cofunction

csc ($\frac{\pi}{2}$ - θ)

sec θ

Cofunction

sec ($\frac{\pi}{2}$ - θ)

csc θ

Cofunction

cos ($\frac{\pi}{2}$ - θ)

sin θ

Cofunction

sin ($\frac{\pi}{2}$ - θ)

cos θ

Cofunction

cot ($\frac{\pi}{2}$ - θ)

tan θ

Reciprocal

cot θ

$$\frac{1}{\tan\theta}$$

Reciprocal

sin θ

$$\frac{1}{\csc}$$

Reciprocal

cos θ

$$\frac{1}{\sec\theta}$$

Reciprocal

csc θ

$$\frac{1}{\sin\theta}$$

Reciprocal

tan θ

$$\frac{1}{\cot\theta}$$

Reciprocal

sec θ

$$\frac{1}{\cos\theta}$$

Quotient

tan θ

$$\frac{\sin\theta}{\cos\theta}$$

Quotient

cot θ

$$\frac{\cos\theta}{\sin\theta}$$

Sum

cos (α+β)

cos α cos β - sin α sin β

Sum

sin (α+β)

sin α cos β + sin β cos α

Double Angles

sin (2θ)

2sin θ cos θ

Double Angles

tan (2θ)

$$\frac{2\tan\theta}{1-\tan^2\theta}$$

Double Angles

cos (2θ)

cos²θ-sin²θ

2cos²θ-1

1-2sin²θ

Pyth

sin²θ+cos²θ

1

Pyth

1+tan²θ

sec²θ

Pyth

1+cot²θ

csc²θ

r=1

cot θ

$$\frac{x}{y}$$

r=1

csc θ

$$\frac{1}{y}$$

r=1

sin θ

y

r=1

cos θ

x

r=1

sec θ

$$\frac{1}{x}$$

r=1

tan θ

$$\frac{y}{x}$$

Diff

sin (α-β)

sin α cos β - sin β cos α

Diff

cos(α-β)

cos α cos β + sin α sin β

r≠1

csc θ

$$\frac{r}{y}$$

r≠1

tan θ

$$\frac{y}{x}$$

r≠1

cos θ

$$\frac{x}{r}$$

r≠1

sin θ

$$\frac{y}{r}$$

r≠1

sec θ

$$\frac{r}{x}$$

r≠1

cot θ

$$\frac{x}{y}$$

Domain

y=sin(x)

Range

y=sin(x)