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It is given that A is an obtuse angle and cosA=-sqrt5/3.

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Without using calculator,find the value of cos 3A

 

 
asked Jul 14, 2013 in TRIGONOMETRY by anonymous Apprentice

1 Answer

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cosA=-sqrt5/3.

Using formula cos3A=4cos^3A-3cosA

Substitute -sqrt5/3 for cos A

cos3A=4(-sqrt5/3)^3-3(-sqrt5/3)

            =-4(5sqrt5/3)+3sqrt5/3

             =-20sqrt5/3+3sqrt5/3

             =-17sqrt5/3

answered Jul 14, 2013 by bradely Mentor

cos A = - √5/3.

cos (3A) = 4cos3 A - 3cos A

= 4(- √5/3)3 - 3(- √5/3)

= - 4(√5/3)3 + √5

= [(- 4 * 5 * √5)/27] + √5

= √5[ - 20/27 + 1]

= √5(- 20 + 27)/27

= 7√5/27.

Therefore, cos (3A) = 7√5/27.

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