Trigonometric Equations and Identities

An equation involving only algebraic expressions

An equation that contains a trigonometric expression with a variable

An equation that contains no variables

An equation that involves only linear functions

Divide both sides by sin(x)

Add 3sin(x) to both sides

Subtract 3sin(x) from both sides

Multiply both sides by 2

x = π/3 + 3nπ, where n is any integer

x = π/3 + nπ, where n is any integer

x = π/3 + 2nπ, where n is any integer

x = π/3 + 4nπ, where n is any integer

No trigonometric functions

A single trigonometric function

Multiple trigonometric functions

A number attached to the variable

x = π/2, 3π/2

x = π/4, 3π/4

x = π/6, 5π/6

x = π/3, 4π/3

By using the sine and cosine rules

By using the Pythagorean identity

By using the square root property

By using the quadratic formula

Multiply both sides by 4

Subtract 3 from both sides

Divide both sides by 4

Add 3 to both sides

Adding sin(x) to both sides

Subtracting sin(x) from both sides

Multiplying both sides by sin(x)

Dividing both sides by sin(x)

If a product is zero, neither factor can be zero

If a product is zero, the product must be negative

If a product is zero, one of the factors must be zero

If a product is zero, both factors must be zero

By adding a constant to both sides

By multiplying both sides by a variable

By dividing both sides by a constant

By substituting a known identity