Learn to solve multiple angles in trigonometry

👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include by factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given equation. Simpler trigonometric equations involving one trigonometric function can simply be solved by inverse operations.

When solving a trigonometric equation it is usually useful to identify which method best evaluates the given equation and apply the method. Because trigonometric functions are sinusoidal in nature (continuous and repetitive), a trigonometric equation may contain many solutions depending on the domain of consideration.

When the trigonometric equation involves multiple angles, the trigonometric equation is evaluated first, and then the multiple of the angle is then divided through the obtained answer.

Organized Videos:
✅ Solve Trigonometric Equations
✅ Solve Trigonometric Equations by Factoring GCF
✅ Solve Trigonometric Equations by Zero Product Property
✅ Solve Trigonometric Equations by Factoring
✅ Solve Trigonometric Equations by Taking the Square Root
✅ Solve a Trig Equation with Half Angles
✅ Solve a Trigonometric Equations with Multi Angles Squared
✅ Solve Trigonometric Equations all Solutions and on an Interval
✅ Solve Trigonometric Equations with Multi Angles
✅ Solve Trigonometric Equations Learn About

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[geeta]

Just wanted to make sure I was following you correctly....n seriously I should be the one thanking you...i invested about two hours working on a problem...and after watching just one video of yours i did it in five minutes....

[brianmclogan]

great question. Actually sin(2x) = 2sin(x)cos(x) There is a proof for it. It depends on the angle that you evaluate for sin(x) Sin(2x) will equal. The reason why we rationalize the denominator is because the root of a non square number is irrational. So you cannot divide a number by a irrational number. Think of dividing a number by pi. It goes on and on and on. So we rationalize the denominator to provide an answer that is exact without dividing by an irrational number. Did this help?

[brianmclogan]

that is great happy to help. Sorry for the confusion and thank you so much for pointing it out to me. Don't want to confuse others

[brianmclogan]

I found it. YES, thank you I made a mistake and made a correction using annotations. You have to take the positive and negative of your even root. I lost track of what I was doing. Thank you Thank you

[sosoliwa]

Really a
I understand your point Thant you for that
But I had a question before even watching this video which is why didn’t restrict it to -90&90 because the inverse of sine is between that
And again thank you, I hope you answer my question after 5years of aploading it

[geeta]

Just curious...sin(2x) can also have the value of (-1/root

Also..(not that it's completely related to trigonometry) but why can't we leave it root 2 in the denominator....why write "root 2/2" and not "1/root 2"

Thanks a ton...Very clear speech...I intend on watching the whole series...

[geeta]

Thanks...I get why we rationalize the denominator...makes sense!
As in if x square = 4 then x= +/- 2 ....by the same logic wouldn't we have sin(2x) = + / - 1/root 2
I'm aware of the formulae...(I did put in -pi/8 in your given equation...and the two sides work out to be equal)

[wernerheisenberg]

Wouldn't it be better to write all possible solutions with one formula? We know that:

sin^2 (2x) = 1/2

and let 2x=a

so sin(a) is +/- sqrt(2)/2. It corresponds to a 45* angle (I had to pick an angle between 0 and 90 degrees to set a starting point), which is written as pi/4 in radians. Now we know that we are looking for either positive or negative sin(a) such that an absolute value of this is sqrt(2)/2.

If you draw a trigonometric circle it is easy to see that we just move from pi/4 to 3pi/4 (those are positive sines) and then to 5pi/4, 7pi/4 (those are negative sines), and so on. In other words - we can write our solution as moving from pi/4 by 90 degrees n times (3pi/4 is the same as pi/4 moved by 90 degrees, and 5pi/4 is the same as 3pi/4 moved by 90 degrees or pi/4 moved by 180 degrees, which is two times 90 degrees).

So: sin(a)= +/- sqrt(2)/2 if a = pi/4 + n*pi/2

Therefore:

2x = pi/4 + npi/2 => [ x = pi/8 + n*pi/4 ]


And by doing this we have compressed our solution into a single formula.

[basilmcpherson]

On the internal 0 to 2pi are there more solutions than you found in the video

[adacotto]

Hi Professor, I'm lost on this exercise. Not sure where the result 2X/2= pi/4 =pi/8 + 2pi n came from. Would it be possible for you to explain this part for me? I understood everything up to that point. Looking at the unit circle I can tell that the values pi/3 and pi/4 are the equivalent of y value 2sqrt/2, right? ...But that's it! :-(

[wristdisabledwriter]

Oh I was thinking of switching the sin2x to 2sinxcosx but couldn’t figure out out to solve from there this makes sense