Proof of sen² 25º + cos² 45º + sen² 65º = 3/2

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SUMMARY

The equation sen² 25º + cos² 45º + sen² 65º simplifies to 3/2. In this discussion, it is clarified that "sen" refers to "sin," and the notation sen² x indicates the square of the sine function, specifically (sin x)². The value of cos 45º is established as 1, which is critical for the calculation. The discussion emphasizes understanding the notation and the trigonometric identities involved.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosine.
  • Familiarity with trigonometric identities and their properties.
  • Knowledge of angle measurement in degrees.
  • Basic algebraic manipulation skills for simplifying equations.
NEXT STEPS
  • Study the unit circle and its application to sine and cosine functions.
  • Learn about trigonometric identities, including Pythagorean identities.
  • Explore the concept of angle addition formulas in trigonometry.
  • Practice solving trigonometric equations and verifying identities.
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Students studying trigonometry, educators teaching mathematical concepts, and anyone seeking to strengthen their understanding of trigonometric identities and equations.

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Homework Statement


Show that sen² 25º + cos² 45º + sen² 65º = 3/2



Homework Equations


cos 45º= 1


The Attempt at a Solution


I get confused with the ² on the cos and sen...
 
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Hi Fanekaz! :smile:

(btw, it's sin, not sen :wink:)
Fanekaz said:
I get confused with the ² on the cos and sen...

It just means that the whole thing is squared …

so sin2x means (sinx)2 …

(pronounce it "sine squared of x")

it saves writing brackets. :biggrin:​
 

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