# 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.