Double angle trig

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Referring to Q7 in Hinemann 2004, Given cos x = -1/3, use an appropriate double angle formula to find the exact value of sec2x?

Posted Thu 17th January, 2013 @ 02:11 by Mohamad Qadoomy

2 Answers

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sec2x is the same as 1/cos2x.

Now use the double angle formula for cos 2x on the denominator and see if you can go on from there.

Answered Thu 17th January, 2013 @ 16:48 by usycool1
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cosx= -1/3

sec2x = 1/(cos2x)

all variations of the the cos2x identity are taken from the identity that cos2x = cos^2(x)-sin^(2)x

so we know that cosx=-1/3

now using pythagoras we can find what sinx is.

since cos= A/H we know that the adjacent is -1 and the hypotenuse is 3.

to work out the other side ''x'' we need to do (3)^2 - (-1)^2 and then root this answer.

this gives us the value of x as 2root2

this means that the opposite is 2 root 2.

since sin = OH = opposite/hypotenuse,  sinx = 2root2/3

ok now we know that 

cosx= -1/3

sinx= 2root2 /3

now use the identity I stated at the beginning

cos2x= (-1/3)^2 - (2root2/3)^2 = -(7/9)

so cos2x = -7/9

now we need to find sec2x

cos2x = 1/sec2x

so to find the answer we just do the inverse of -7/9

this gives the answer as -9/7

so sec2x= -9/7

hope this helped (I did this without writing anything down so it'd be worth checking over what I've done)

Answered Sun 20th January, 2013 @ 19:40 by .