Math Analysis – Trigonometric Equation on an Interval

By | September 7, 2016

Trigonometric Equation on an Interval

In this tutorial the students will learn how to solve a trigonometric equation on an interval.  The student should be familiar with interval notation, the unit circle, trigonometric ratios, properties of Algebra and basic Algebra operations used to solve equations.

Key skills

Interval Notation

[ and ] are inclusive

( and ) are exclusive

Unit Circle

The x coordinate corresponds to cosine.

The y coordinate corresponds to sine.

(x,y) ==> (cos θ,sin θ)


0 radians at (1,0):  cos(0) = 1, sin(0) = 0

π/2 radians at (0,1): cos(π/2) = 0, sin(π/2) = 1

π radians at (-1,0): cos(π) = -1, sin(π) = 0

3π/2 radians at (o,-1): cos(3π/2) = 0, sin(3π/2) = -1

2π radians at (1,0): cos(2π) = 1, sin(2π) = 0

Trigonometric Ratios

sin(θ) = y/r

cos(θ) = x/r

tan(θ) = y/x

tan(θ) = sin(θ)/cos(θ) = y/x

Algebra Properties

Zero Product Property which basically states that if any of the factors are zero then the product is zero.

Algebra Skills

When terms move across the equal sign then the sign of the term changes to its opposite.

Click Solving a Trigonometric Equation on an Interval for another example.