Trigonometric Equations

Question

What are the solutions to the equation 4sin(2x+5) + 3 = 3 - 2√2 in the interval [0, 360°)?

Give the solutions in degrees.

Answer 1

Mark, you're off your game today!

Yes, sin -45 is -√2/2, but the question asked for all solutions between 0 and 360. So, if x can be anywhere from 0 to 360, then 2x can be anywhere from 0 to 720, and x would still be in the interval. And x can't be -25, because that's less than zero.

So, Destiny, you'll have to figure out:

 

- The next angle that works.  If it's not -45, then what's an allowable angle with a sine of -√2/2?

- Is there any other angle between 0 and 360 that would have the same sine?  They usually come in pairs, from two different quadrants.

 

For both of those angles, Mark gave the equation that you need to solve:  2x + 5 = (the angle you've figured out).

 

- Once you have those two answers for x, you can now find other values of x that are still in the allowable interval.  For example, if one of your original angles was 225 degrees, could you go around the circle again by adding 360 and still end up with an x that is okay?

 

Hope this helps.

 

Answer 2

4sin(2x + 5) + 3 = 3 - 2√2

4sin(2x + 5) = -2√2

sin(2x + 5) = -√2 / 2

   sin -45° = -√2 / 2

2x + 5 = -°45

2x = -50°

x = -25°