Solving Trig Equations

Notes 5-

Solving Trig Equations

By John Campbell

Warm-Up

Multiple Choice

Evaluate the trigonometric ratio for the given angle in simplest form.

Multiple Choice

Evaluate the trigonometric ratio for the given angle in simplest form.

Multiple Select

Find all answers to the equation in standard position.

Multiple Select

Find all answers to the equation in standard position.

Multiple Select

Find all answers to the equation in standard position.

Finding Infinite Answers

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Remember all coterminal angles will have the same trig ratios, because they share the same reference angle and quadrant.

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cos(ϴ)= √3/2

has infinite answers.​

Every positive and negative rotation of both standard angle answers.​

"All angles coterminal to standard answers."​

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Open Ended

In your own words tell me all the answers to $$\sin\left(\theta\right)=\frac{1}{2}$$  

Poll

Which of the following equations do you think represent all possible answers to...

$$\sin\left(\theta\right)=\frac{1}{2}$$  ?

• $$30^{\circ}+360^{\circ}n$$  , n=integers

• $$330^{\circ}+360^{\circ}n$$  , n=integers

• $$150^{\circ}+360^{\circ}n$$  , n=integers

• $$210^{\circ}+360^{\circ}n$$  , n=integers

Practice

Multiple Select

Find all answers to the equation.

Multiple Select

Find all answers to the equation.

Multiple Select

Find all answers to the equation.

NOTICE: We could write all the answers to the last question with only one equation.

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Solving multiple step trig equations.

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Draw

Attempt the following:

Write your answers to $$\sin^2\theta=\frac{3}{4}$$  ? Give all posible answers in standard position.

Multiple Select

If $$\sin^2\theta=\frac{3}{4}$$  , then which of the following would equal $$\sin\theta$$  ?

• $$-\frac{\sqrt[]{3}}{2}$$  

• $$\frac{\sqrt[]{3}}{2}$$  

• $$\frac{9}{16}$$  

• $$\frac{\sqrt[]{3}}{4}$$  

Multiple Select

Concidering your answer to the previous question, which of the following would equal $$\sin^2\theta=\frac{3}{4}$$  ?

•    $$120^{\degree}$$  

• $$60^{\degree}$$   

•   $$240^{\degree}$$  

•   $$300^{\degree}$$  

Using substitution to solve trig equations.

Let's try solving a quadratic trig equation.

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Fill in the Blanks

STEP 1

If we let x = $\tan\theta$  , then using substitution $4\tan^2\theta+\tan\theta-3=0$   could be written...

Fill in the Blanks

STEP 2

Type the factored form of $4x^2+x-3=0$  

Fill in the Blanks

STEP 3

Solve for x when (4x-3)(x+1)=0

x=

Multiple Select

STEP 4

If $$x=\tan\theta$$  and x= 3/4 , -1 , then...

• $$\tan\theta=\frac{3}{4}$$  

• $$\tan\theta=135^{\degree}$$  

• $$\tan\theta=-1$$  

• $$\tan\theta=315^{\degree}$$  

Open Ended

FINAL STEP

Solve for all values $$\theta$$  in standard position if $$4\tan^2\theta+\tan\theta-3=0$$  

Open Ended

INFINITE ANSWERS

Solve for all values $$\theta$$   if $$4\tan^2\theta+\tan\theta-3=0$$