## 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**

Thex coordinatecorresponds tocosine. They coordinatecorresponds tosine. (x,y) ==> (cos θ,sin θ)0 radiansat (1,0): cos(0) = 1, sin(0) = 0 π/2 radiansat (0,1): cos(π/2) = 0, sin(π/2) = 1 πradiansat (-1,0): cos(π) = -1, sin(π) = 03π/2 radiansat (o,-1): cos(3π/2) = 0, sin(3π/2) = -12π radiansat (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.

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