Tips for Solving Half Angle Identities with Horizontal Shifts

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SUMMARY

The discussion focuses on solving half angle identities involving horizontal shifts, specifically the identity tan(1/2(ß + π/2)) = (1 + sin(ß)) / cos(ß). The user seeks guidance on handling horizontal shifts in trigonometric functions, particularly how the sine and cosine graphs behave when shifted left by π/2 radians. The key takeaway is understanding the transformation of trigonometric functions under horizontal shifts to effectively apply half angle identities.

PREREQUISITES
  • Understanding of half angle identities in trigonometry
  • Familiarity with basic trigonometric functions: sine and cosine
  • Knowledge of horizontal shifts in function graphs
  • Ability to manipulate trigonometric equations
NEXT STEPS
  • Study the properties of sine and cosine functions under horizontal shifts
  • Practice solving half angle identities with various transformations
  • Explore the unit circle to visualize trigonometric function shifts
  • Learn about the graphical representation of trigonometric identities
USEFUL FOR

Students studying trigonometry, educators teaching half angle identities, and anyone looking to deepen their understanding of trigonometric transformations.

dranseth
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Homework Statement


I'm on the last section of identities entitled half angle identities. This one seems to give me some trouble because I have never encountered one with a horizontal shift in it. Tips?

tan 1/2( ß + π/2 ) = ( 1 + sin ß ) / cos ß
 
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Recall that:

\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}

Now, what do the graphs of the sine and cosine functions look like when you shift them to the left by \frac{\pi}{2} rad?
 

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