(Solved) Triginomotery highschool level.

hellohi

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12 years ago

Hi there, just need some quick help. I can do the basic questions in my textbook, but not this one.
The angle x lies in the interval pi/2 and pi, and sin^2 x=8/9. Without a calculator determine the value of cosx/2 using a double angle formulas. ..

and samething but with sin3x. I guess its cause I don't know how to convert, please help and thanks:)

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BearPro

wrote...

Valued Member

12 years ago

Quote from: hellohi (12 years ago)

cos2(x/2) = (1+cos x)/2 ......... double angle formula

now sin2(x) = 8/9
so cos2(x) = 1-8/9 = 1/9
so cox (x) = -1/3 [ and not 1/3) because for angles lying between pi/2 to pi,
cos x is negative.
so x/2 lies between pi/4 to pi/2,
in this interval, cos(x) is positive.
so cos(x/2)= under root[(1-1/3)/2]
which equals cos (x/2) = sq rt(1/3)

you might like to see this presentation on trigonometryhere

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duddy

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12 years ago

Amazing response by our mathematics expert, please mark as solved.

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BearPro

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Valued Member

12 years ago

thanks duddy.
marking the topic as solved.

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