# 5.3.2 Linear Trigonometric Equations

#### Solving linear trigonometric equations

• You should have already seen two ways to solve linear trig equations
• By sketching the graph (see Graphs of Trigonometric Functions) you can read off all the solutions in a given range (or interval)
• By using trigonometric identities you can simplify harder equations
• Another way to find solutions is by using the CAST diagram which shows where each function has positive solutions

#### What about more complicated trig equations?

• Some trig equations could involve a function of x or θ (see Transformations of Trigonometric Functions)
• Functions could be in two forms, either y =  sin(θ ± k) or y = sin kθ
• An easy way to solve an equation involving sin, cos or tan of (θ± k) or kθ is by transforming the range of the question

#### Exam Tip

Your calculator will only give you the principal value and you need to find all other solutions for the given interval. Also, remember the CAST diagram only gives you some solutions, so again you may need to find more depending on the given interval.

It is entirely up to you how you solve a trig equation, but some ways are more helpful than others depending on the type of equation you are trying to solve

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