How do we solve linear trigonometric equations?

How do we solve linear trigonometric equations?

So when you solve linear trigonometric equations your just solving for any variable or θ.

There are 3 simple steps to solving, but let's do a quick practice to prepare.

Let's find the degrees of 2Sinθ-1 = 0

So you first add 1 to both sides and the divide by 2 to get Sinθ by itself

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So you'd get Sinθ = 1/2

We know that Sin equals y, so then we'd find out where Sin is equal to 1/2. 

                   

According your trigonometric circle, you'd look to see where the point y is equal to 1/2.  *There's always two points, so look closely on the opposite side*

Or another shortcut is plugging the equations above in the calculator. You would have to find the inverse of Sinθ = (1/2) →  Sin⁻¹(1/2) = θ

You'd get 30°, so you have to subtract 180° and make it positive no matter what to get the second answer. Which is 150°

⤤ This method above only works for Sin, so be careful. 

Back on Track !!

Let's talk about those 3 steps then. 

1. Get the Trig function alone

Trig functions are Sin, Cos, Tan, etc. 

2. Use inverse of function to solve for angle

So when we did the inverse of Sin to find the angle of θ, that's what I mean.

3. Check for other solutions

Just like we found a shortcut but we looked for other solution once we got 30°, then we found 150°

Most of the time a problem is going to give you a range in where the answer could be. Let's try this sample problem.

Solve for all values that 0 ≤ θ ≤ 2π :

2Sinθ = √3

So you divide both sides by to to get Sinθ alone.

Sinθ = √3 / 2

Now you do the inverse of Sin ( Sin⁻¹ ) with √3 / 2 to get the angle of θ.

θ = 60°

So we have to check for other solutions, and we get 60° and 120°.

All using the 3 simple steps !! 

Sources:

1. John Schnatterly: johnschnatterly.blogspot.com