5.5 Trigonometric Equations

To solve an equation containing a single trig function:

1. Isolate the trig function on one side of the equation. 2. Solve for the variable.

_____________ are used to solve some trig equations. In order to solve a trig equation, we need one trig function of the _____________ angle.

Identities, same

Solution(s)

The value(s) that make an equation true.

_____________ can be used to separate _____________ different trig functions in an equation.

factoring, two

Some trig equations are solved using the calculator's ______________ trig functions such as ________________.

inverse, tan⁻¹

When solving equations involving ___________ angles, the _____________ plays an important role in ensuring that we do not leave out any solutions.

multiple, period

Trig equations in _______________ form can be expressed as au² + bu + c = 0, where u is a trig function and a ≠ 0. Such equations can be solved by _______________, the square root property, or the quadratic formula.

quadratic, factoring

To use the square root property

If u² = c, then u = √c or u = - √c

To solve by factoring

Set the equation equal to zero, factor, and set each factor to zero.

To use the Quadratic formula

Set the equation to zero, identify a, b, and c. x = (-b ± √(b² - 4ac) )/(2a)

Trigonometric Equation

an equation that contains a trigonometric expression with a variable, such as sin x.