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General Solutions of Trigonometric Equations (Radians)

Updated: Mar 25, 2023

π rad = 180°

Using radian mode on the calculator you can solve an equation and give answers either in decimals or multiples of π. For radian equations, the three formulas for general solutions are:

These are analogous to the formulas for degrees.


Example

Solve for 0≦x≦π the equation

Using the sine formula,

n=0 ⇒ x=1.74 rad

n=1 ⇒ x=2.97 rad

 

Example

Giving your answers as multiples of π, solve for 0≦x≦2π the equation

Using the cosine formula,

n=1 ⇒ x=23/24π, 19/24π

n=2 ⇒ x=47/24π, 43/24π

 

Example

Giving your answers as multiples of π, solve for 0≦x≦4π the equation

Using the tan formula,

n=0 ⇒ x=π/3

n=1 ⇒ x=7π/3, 5π/3

n=2 ⇒ x=11π/3

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