Question
upstudy study bank question image url

2. If Bin \( 9=a \), find \( \sin 18^{\circ} \) interms of \( a \), without using cancuator and with ait of a diagram

Ask by Reid Wilson. in South Africa
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

\(\sin 18^\circ = \frac{a - 1}{4}\)

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

Mind Expander

To find \( \sin 18^{\circ} \) in terms of \( a \) (where \( a = \binom{9}{2} \)), we first recognize that \( a = \frac{9!}{2!(9-2)!} = \frac{9 \times 8}{2 \times 1} = 36 \). From trigonometric identities, we can use the fact that \( \sin(18^{\circ}) = \frac{\sqrt{5} - 1}{4} \). To express this in terms of \( a \), we set up the equation \( 36 = 4(\sqrt{5} - 1) \). Thus, \( \sin 18^{\circ} = \frac{a}{9} + \frac{1}{4} \). Check if your diagram includes a pentagon, as this could help visualize \( 18^{\circ} \) as an internal angle. The golden ratio also plays a role here since \( \sin 18^{\circ} \) relates to the properties of a regular pentagon! Drawing lines connecting the vertices can make the relationship clearer and show how \( \sin 18^{\circ} \) appears in geometrical figures.

Related 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