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! #17

Complex Numbers. As if numbers weren't already complicated, there exist complex numbers. When did that happen and why? 🤷🏿😂🤦🏿‍♀️ I'm going a bit lite in this week's problem. (At least, I think it's lite.)

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

    ✔️  How to deal with imaginary numbers

    ✔️  How to multiply conjugates

    ✔️  How to square fractions

    

Here is WMP! #17...

Happy solving! 

Check back on Friday, August 28th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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Did you find the problem annoying? You can tell the truth. This is a no-judgment zone. Listen, a problem like this requires your attention because mistakes can easily be made. Did I find it annoying? Well, I didn't find it the opposite of annoying and that's my answer. 😁

I did the problem in two parts. The first part was just the squaring and simplification of the rational expression:

Once that was completed, I proceeded to the second part which consisted of rationalizing the denominator of the result:

I definitely did not get this on the first try. How did I know that I was incorrect on the first try? I used Mathway - Algebra to check my answer, because I know with all of those negative signs floating around, I could've easily made a mistake...and I did. So, I went back and searched my work to locate the error. These are the kind of problems a teacher would give as extra credit. 😅

◾️ How did you feel about squaring fractions and rationalizing the denominator?? 

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

Are we up to WMP! #18 already?

Cheers!

The Younge Lady