How Do You Solve for Sin(theta/2) Using the Half Angle Formula?

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SUMMARY

The discussion focuses on solving for sin(theta/2) using the Half Angle Formula, given that sin(theta) = 3/5 and 0 < theta < π/2. The user initially derived the expression as the square root of (1 - 3/5) / 2. The solution simplifies to the square root of 1/5, which is confirmed by the community. The user acknowledges their initial confusion and attributes it to sleep deprivation.

PREREQUISITES
  • Understanding of the Half Angle Formula in trigonometry
  • Basic knowledge of sine function values
  • Ability to manipulate square roots and fractions
  • Familiarity with the unit circle and angle measures in radians
NEXT STEPS
  • Study the derivation and application of the Half Angle Formula in trigonometry
  • Practice problems involving sine and cosine values
  • Explore the relationship between sine and cosine using the Pythagorean identity
  • Learn how to simplify square root expressions in trigonometric contexts
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Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to enhance their understanding of the Half Angle Formula.

daliberataaa!
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Homework Statement


given that sin theta = 3/5, 0 < theta < pi/2 find sin theta/2


Homework Equations


http://www.intmath.com/Analytic-trigonometry/sinalphaon2.gif


The Attempt at a Solution


I appologize that I don't know how to use all the symbols on a keyboard (square roots, etc)
But I have so far gotten it to :

square root of 1-3/5 all over 2. I have a sample of this same problem in my book, but they don't explain the next step. Suddenly this problem from here just turns into square root of 1/5...can someone please explain how they got to there?

Thank you all.
 
Last edited by a moderator:
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ok i feel like the biggest idiot in the world...i got it.

I blame sleep deprivation...haha.
 

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