SOLVING TRIGONOMETRIC EQUATIONSDr. Shildneck

Spring, 2015

BASIC TRIG EQUATIONS Trigonometric Equations have infinitely many

(specific) solutions. To make things easier (for us) we will

concentrate on only those solutions between zero and two-pi.

To solve trigonometric equations we will utilize traditional methods of solving including, Adding and Subtracting Multiplying and Dividing Factoring Taking Square Roots

OUR PROCESS1) Analyze the equation

a) If the equation has one single trig function, get it by itself.

b) If the equation has multiple of one type of trig function, all of those on one side and re-analyze the equation.

c) If the equation has different trig functions, see if you can factor or perform some operation to separate them.

d) If the equation has different trig functions and you cannot separate them, you will need to use trig identities to convert something.

2. Solve the equation for the trig function (isolate the trig function). This means to get it in a form like: sin(x) = a number To do so, you might need to factor, add, divide or take a

square root, etc.

3. UNIT CIRCLE TIME! Ask yourself: “When does this trig function equal this value?”

4. For Basic Trig Equations, this is your answer. If the angle has a multiplier (like 4x or 2θ), there is more to do. We

will learn about this later in the unit.

TODAY: BASIC TRIG EQUATIONSToday we will examine how to solve trigonometric equations that involve the following.

1. Only one trig function

2. Only one type of trig function

3. Multiple, different trig functions that can be separated algebraically.

EX 1

3sin

2x

WHERE on the unit circle (first positive rotation) is the SINE equal to ?

32

EX 1

3sin

2x

EX 1

3sin

2x

WHERE on the unit circle (first positive rotation) is the SINE equal to ?

32

So, the angles where the SINE is are: 3

2

2 and

3 3

EX 2 2sin 1 0x

EX 3 sec 2 0x

EX 4 3 tan 1 0x

EX 5 3sin 2 5sin 1x x

EX 6 24cos 1 0x

EX 7 22cos cos 1 0x x

EX 8 2tan sin 3tanx x x

ASSIGNMENT

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