# What is formula for Sin2x

## Trigonometric Identities and Formulas

Below are some of the most important definitions, identities and formulas in trigonometry.

## Trigonometric Functions of Acute Angles

sin X = opp / hyp = a / c , csc X = hyp / opp = c / a

tan X = opp / adj = a / b , cot X = adj / opp = b / a

cos X = adj / hyp = b / c , sec X = hyp / adj = c / b ,## Trigonometric Functions of Arbitrary Angles

sin X = b / r , csc X = r / b

tan X = b / a , cot X = a / b

cos X = a / r , sec X = r / a## Special Triangles

Special triangles may be used to find trigonometric functions of special angles: 30, 45 and 60 degress. ## Sine and Cosine Laws in Triangles

In any triangle we have:

1 - The sine law

sin A / a = sin B / b = sin C / c

2 - The cosine laws

a^{ 2}= b^{ 2}+ c^{ 2}- 2 b c cos A

b^{ 2}= a^{ 2}+ c^{ 2}- 2 a c cos B

c^{ 2}= a^{ 2}+ b^{ 2}- 2 a b cos C## Relations Between Trigonometric Functions

cscX = 1 / sinX

sinX = 1 / cscX

secX = 1 / cosX

cosX = 1 / secX

tanX = 1 / cotX

cotX = 1 / tanX

tanX = sinX / cosX

cotX = cosX / sinX## Pythagorean Identities

sin^{ 2}X + cos^{ 2}X = 1

1 + tan^{ 2}X = sec^{ 2}X

1 + cot^{ 2}X = csc^{ 2}X## Negative Angle Identities

sin(-X) = - sinX , odd function

csc(-X) = - cscX , odd function

cos(-X) = cosX , even function

sec(-X) = secX , even function

tan(-X) = - tanX , odd function

cot(-X) = - cotX , odd function## Cofunctions Identities

sin(π/2 - X) = cosX

cos(π/2 - X) = sinX

tan(π/2 - X) = cotX

cot(π/2 - X) = tanX

sec(π/2 - X) = cscX

csc(π/2 - X) = secX## Addition Formulas

cos(X + Y) = cosX cosY - sinX sinY

cos(X - Y) = cosX cosY + sinX sinY

sin(X + Y) = sinX cosY + cosX sinY

sin(X - Y) = sinX cosY - cosX sinY

tan(X + Y) = [ tanX + tanY ] / [ 1 - tanX tanY]

tan(X - Y) = [ tanX - tanY ] / [ 1 + tanX tanY]

cot(X + Y) = [ cotX cotY - 1 ] / [ cotX + cotY]

cot(X - Y) = [ cotX cotY + 1 ] / [ cotY - cotX]## Sum to Product Formulas

cosX + cosY = 2cos[ (X + Y) / 2 ] cos[ (X - Y) / 2 ]

sinX + sinY = 2sin[ (X + Y) / 2 ] cos[ (X - Y) / 2 ]## Difference to Product Formulas

cosX - cosY = - 2sin[ (X + Y) / 2 ] sin[ (X - Y) / 2 ]

sinX - sinY = 2cos[ (X + Y) / 2 ] sin[ (X - Y) / 2 ]## Product to Sum/Difference Formulas

cosX cosY = (1/2) [ cos (X - Y) + cos (X + Y) ]

sinX cosY = (1/2) [ sin (X + Y) + sin (X - Y) ]

cosX sinY = (1/2) [ sin (X + Y) - sin[ (X - Y) ]

sinX sinY = (1/2) [ cos (X - Y) - cos (X + Y) ]## Difference of Squares Formulas

sin^{ 2}X - sin^{ 2}Y = sin(X + Y)sin(X - Y)

cos^{ 2}X - cos^{ 2}Y = - sin(X + Y)sin(X - Y)

cos^{ 2}X - sin^{ 2}Y = cos(X + Y)cos(X - Y)## Double Angle Formulas

sin(2X) = 2 sinX cosX

cos(2X) = 1 - 2sin^{ 2}X = 2cos^{ 2}X - 1

tan(2X) = 2tanX / [ 1 - tan^{ 2}X ]## Multiple Angle Formulas

sin(3X) = 3sinX - 4sin^{ 3}X

cos(3X) = 4cos^{ 3}X - 3cosX

sin(4X) = 4sinXcosX - 8sin^{ 3}XcosX

cos(4X) = 8cos^{ 4}X - 8cos^{ 2}X + 1## Half Angle Formulas

sin (X/2) = + or - √ ( (1 - cosX) / 2 )

cos (X/2) = + or - √ ( (1 + cosX) / 2 )

tan (X/2) = + or - √ ( (1 - cosX) / (1 + cosX) )

= sinX / (1 + cosX) = (1 - cosX) / sinX## Power Reducing Formulas

sin^{ 2}X = 1/2 - (1/2)cos(2X))

cos^{ 2}X = 1/2 + (1/2)cos(2X))

sin^{ 3}X = (3/4)sinX - (1/4)sin(3X)

cos^{ 3}X = (3/4)cosX + (1/4)cos(3X)

sin^{ 4}X = (3/8) - (1/2)cos(2X) + (1/8)cos(4X)

cos^{ 4}X = (3/8) + (1/2)cos(2X) + (1/8)cos(4X)

sin^{ 5}X = (5/8)sinX - (5/16)sin(3X) + (1/16)sin(5X)

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