Question
upstudy study bank question image url




  1. 5






Ask by John Mejia. in South Africa
Mar 17,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The solutions are:
  • with or for any integer .
  • or .

Solution

  1. Begin with the equation
  2. Isolate the cosine term by subtracting 3 from both sides:
  3. Divide both sides by 5:
  4. The general solutions for an equation of the form
    are given by
    where is any integer.
    Thus, for
    the solutions are
  5. It appears that the subsequent steps involve the equation of a circle,
    If we interpret the value as the -coordinate on a circle with radius , then substitute and into the circle’s equation:
  6. Compute:
  7. Solve for :
  8. Take the square root of both sides. Remember that both positive and negative roots are possible:
Thus, the solutions are:
  • For the trigonometric equation:
  • For the circle equation with and :

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Beyond the Answer

Oops! Seems like there’s a little mix-up here. While your manipulation of the cosine equation is on track, you took a wrong turn when you ventured into the sine territory. Remember, tells you about the x-coordinate on a unit circle, while would relate to the y-coordinate. So instead of , let’s stick with the original cosine pathway!
Now, about the circle equation—you’ve got that part right! So after finding that , you can determine the angle that corresponds to that cosine value. Dig into your trigonometric identities and fear not, for angles in the second and third quadrants will fit the bill!
Watch out for common mistakes! Misplacing your sine and cosine can lead to a real head-scratcher. Make sure you stay on the right function path. When dealing with circular coordinates, remember which trigonometric function corresponds to which axis— for x and for y. It’ll save you from going on a wild goose chase!

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy