Question
upstudy study bank question image url

(7) \( \tan \alpha=\cos \alpha \)

Ask by Peters Elliott. in South Africa
Mar 15,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The solutions to the equation \( \tan \alpha = \cos \alpha \) are: \[ \alpha = \arcsin\left(\frac{-1+\sqrt{5}}{2}\right) + 2k\pi \] \[ \alpha = -\arcsin\left(\frac{-1+\sqrt{5}}{2}\right) + \pi + 2k\pi \] where \( k \) is any integer.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

The Deep Dive

Did you know that the equation \( \tan \alpha = \cos \alpha \) can be transformed into a trigonometric identity that reflects the intersection of different trigonometric functions? By rearranging the equation, we can derive that \( \sin \alpha = \cos^2 \alpha \), leading us to insights about angles where sine values are equal to the square of their cosine counterparts! Now, if you’re solving this equation, a common pitfall is overlooking the intervals where the tangent and cosine functions intersect. Remember, both functions can behave quite differently depending on the angle! Make sure to check for all quadrants and consider the periodic nature of these functions for a comprehensive solution. Happy solving!

Latest Trigonometry Questions

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