Posted by sh on Friday, March 5, 2010 at 3:20am.
Find the value of tan2x, (pi/2)<x<pi, given secx=5/4.
So cosx=4/5? I've no clue what to do next.

Calculus  Reiny, Friday, March 5, 2010 at 7:42am
According to the given domain, the angle must be in quadrant II,
We are given cosx =  4/5.
remember that cosine is adjacent/hypotenuse, so construct a right angles triangle with base of 4 and hypotenuse of 5, you should recognize the 345 rightangled triangle so the height (or opposite) is 3 and
sinx = 3/5
remember that tangent = sine/cosine
and tanx = (3/5)/(4/5) =  3/4
have you come across the identiy
tan 2x = 2tanx/(1  tan^2 x) ?
tan2x = 2(3/4)/(1  9/16)
= (3/2)/(7/16)
= 24/7

Calculus  sh, Friday, March 5, 2010 at 9:55am
Thanks!
Answer This Question
Related Questions
 precal  find all solutions in interval [0,2pi] tanĀ²x = 3/2 secx This question...
 Pre Calculus  Having trouble verifying this identity... cscxtanx + secx= 2cosx ...
 PreCalc  Trigonometric Identities Prove: (tanx + secx 1)/(tanx  secx + 1)= ...
 Calculus 2 Trigonometric Substitution  I'm working this problem: ∫ [1tan...
 Precalculus/Trig  I can't seem to prove these trig identities and would really ...
 precal  1/tanxsecx+ 1/tanx+secx=2tanx so this is what I did: =tanx+secx+tanx...
 PreCalculus  How do you verify: 1.) sinxcosx+sinx^3secx=tanx 2.) (secx+tanx)/(...
 math  1. (sinx/cscx)+(cosx/secx)=1 2. (1/sinxcosx)(cosx/sinx)=tanx 3. (1/1+cos...
 Precalculus  Prove the following identities. 1. 1+cosx/1cosx = secx + 1/secx...
 Trig  If secx = 8 and pi/2 < x < 0, find the exact value of sin2x Use ...
More Related Questions