Help needed with A-Level maths question - Sec, cos and formulas!!
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Help needed with A-Level maths question - Sec, cos and formulas!!

[From: ] [author: ] [Date: 11-11-11] [Hit: ]
.f(x) = 2secx + 2x - 3,where x is in radians.(a). Evaluate f(0.4) and f(0.......
Hiya, i've got an A-level question that I am a little stuck with. I was wondering if anyone would know how to do it...

f(x) = 2secx + 2x - 3, where x is in radians.

(a). Evaluate f(0.4) and f(0.5) and deduce the equation f(x) = 0 has a solution in the interval 0.4
^^^^I've done the above by substituting 0.4 and 0.5 into f(x). One value was negative and the other was positive, therefore, I know that the solution lies in the interval 0.4
However, I have tried, but cannot do the next part, part b (below):


(b) Show that the equation f(x) = 0 can be arranged in the form x = p + q/cosx, where p and q are constants, and state the value of p and q.

Does anyone know how to do part (b)? I would be very grateful for any advice and any help would be very much appreciated! Thankyou xx

-
your reasoning in part a is correct.

b) If f(x) = 0
then 2secx + 2x - 3 = 0
2x = -2secx +3
x = - 1/cosx + 3/2 ( secx = 1/cosx )
this is of the required form and p = 3/2 and q = -1




This is the required form and p = -1 and q = 3/2
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