Trigonometric
Equations
abc
TRIGONOMETRIC
EQUATIONS
A trigonometric equation is one that involves one
or more of the six functions sine, cosine, tangent,
cotangent,
secant,
and
cosecant.
Some
trigonometric equations, like x = cos x, can be
solved only numerically, through successive
approximations. But a great many can be solved
analytically (in “closed form”, an exact solution in
symbols)
METHODS FOR SOLVING
TRIGONOMETRIC EQUATIONS CAN
BE SUMMARIZED AS FOLLOWS
Solving by Linear Methods
Solve the equation 2sin(θ) + 1 = 0
Since sin(θ) = -1/2 is true for
θ = 210° in the III quadant and
θ = 330° in the IV quadrant
The answers are:
θ = 210° and θ = 330°
Solving by Factoring
Solving by using the Quadratic Formula
x = 73.2°
x = 286.8°
Solving by Squaring
Solving by using a Half Angle
Solving by using a Double Angle
Practice