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geometricaly derive the value of  sin 45

Asked by amolshukal.2001 1st February 2018, 9:28 PM
Answered by Expert
Answer:
begin mathsize 16px style Given colon space In space increment ABC comma space angle straight B equals 90 degree space and space angle straight A equals 45 degree
Find colon space Trigonometric space ratios space of space 45 degree
Proof colon space In space increment ABC comma
space space space space space space space space space space space space space angle straight A plus angle straight B plus angle straight C equals 180 degree
space space space space space space space space space space space space space 45 degree plus 90 degree plus angle straight C equals 180 degree
space space space space space space space space space space space space angle straight C equals 45 degree
space space space space space space space space space space space space angle straight A equals angle straight C equals 45 degree
bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space Let space AB equals BC equals straight x
space space space space space space space space space space space space Find space AC space using space Pythagoras comma
space space space space space space space space space space space space AC squared equals AB squared plus BC squared
space space space space space space space space space space space space AC squared equals straight x squared plus straight x squared
space space space space space space space space space space space space AC squared equals 2 straight x squared
space space space space space space space space space space space space AC equals square root of 2 straight x
space space space space space space space space space space space space sinA equals BC over AC equals fraction numerator straight x over denominator square root of 2 straight x end fraction equals fraction numerator 1 over denominator square root of 2 end fraction
space space space space space space space space space space space space angle straight A equals angle straight C equals 45 degree
space space space space space space space space space space space space sinC equals fraction numerator 1 over denominator square root of 2 end fraction


Similarly space you space can space find space out space remaining space trigonometric space ratios. end style
Answered by Expert 2nd February 2018, 9:20 AM
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