Weekly Math Problem! #24

Trigonometric Equation. The last time I had a trigonometric equation on here was back in June, WMP! #8. (Be sure to check it out. 😉)  That trig equation didn't have any of the functions squared. This week's problems involves a squared function and a function with a double angle. I know, I know... Why, Lori?! Because it looked fun to solve. 🤓

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️ Double angle formulas
        ✔️ How to solve quadratic equations
        ✔️ How to isolate the angle in a trigonometric function

By the way, you'll definitely need at least a scientific calculator for this one. Here is WMP! #24:

Happy solving!

Check back on Friday, October 23rd for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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This problem is a quadratic trigonometric equation. What makes it "difficult" to solve is the trigonometric function with the double angle. How do we deal with that? Use a double angle formula to replace it in the equation. Let me show you...

                                                                       

As you can see, switching out the double angle trigonometric function for an equivalent one helped a great deal. It allowed for the original equation to be reduced to a simpler quadratic equation that could be solved with ease...and a calculator...lol 😅.

 

▪️ Did you use the same double angle formula I used to solve?? 

▪️ Comment below with your responses and let me know what you thought about this week's problem.

Thanks for solving with me this week!

See you next week for WMP! #25

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Cheers!

The Younge Lady

Weekly Math Problem! #8

Solving A Trigonometric Equation. So, I kind of like trigonometric equations. When you're learning College Algebra/Precalculus, the trigonometric equations you get pretty much work out nicely--having the same trigonometric functions in them or allowing you to use trig identities to force your equation to have the same trig functions in them...for the most part. Also, the values for the angle(s) you're solving for tend to be those "special" angle values. This week's trig equation is one I don't recall learning in school, but was exposed to while tutoring. 

To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  General form of a trigonometric equation

    ✔️  Pythagorean Theorem

    ✔️  Trigonometric identities

I present to you WMP! #8...

Happy solving! 

Check back on Friday, June 26th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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I preface my solution by saying that the my use of colors is more for me as much as it is for you. I hope that makes sense. 🤷🏿

Here's the thing...in solving this problem, the thing that tripped me up the most is moving from the form of the solution to using the appropriate trigonometric addition identity, denoted in blue towards the top of my solution. May I also point out when solving for Φ (phi), that it is best to use both the sine and cosine functions. If not, you run the risk of possibly solving for a slightly incorrect value of Φ by using just one of the functions. For example, if you used arccos( ), to solve for Φ, you would have gotten a positive value, instead of the negative value needed to substitute in the expression to finish solving for x.

One thing I can surely say is, I feel more comfortable solving a problem that looks like this one. This was good for my brain. Oh, and before I forget...I solved for x in radian measure because it's something that I'm not used to doing. I can think a bit more easily in degrees, so I decided not to solve for x in degrees.

◾️ Are you used to solving these types of trigonometric equations??

◾️ Comment below with your responses and let me know what you thought about this week's problem.

Moving right along to WMP! #9 👍🏿

Cheers!

The Younge Lady