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Grade 12Trigonometry

We find max and min value of

asin@+bcos@ by +-( underroot ( a power2 + b power2))

Can we find the max and min value of asin(2@)+bcos(2@) using the same formula as +-( underroot ( a power2 + b power2)).

Please explain in detail. Urgently..

Profile image of SAAWAN Pawan VERMA
15 Years agoGrade 12
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1 Answer

Profile image of Jaya IITK
ApprovedApproved Tutor Answer15 Years ago

Get into the depth why u use that formula.

Its very important for iit point of view.

c=a sin@ + b Cos@

c/under root(a^2+b^2)= (a /root under(a^2+b^2)) sin@+ (b/root under(a^2+b^2)                                                                                                             cos@

 

If u take a right angled triangle witrh sides a, b then its hypotenues will be under root(a^2+b^2)

 

 

therefore its in the form of:

 

c/root(a^2+b^2) = cos $ sin @ + sin$ cos @

 

c= root(a^2+ b^2) sin($+@)

 

-1<=sin(@+$)<= 1

 

therefore c lies between - root( a^2+b^2) and root(a^2+ b^2)

 

thus u can see even if u replace @ by 2@ u get the same result..

 

Plzzzzzzzzzzz approve my answer!!!!!!!!!