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 3-4-5 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

- Pre Calculus - Having trouble verifying this identity... cscxtanx + secx= 2cosx ...
- Pre-Calc - Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= ...
- Calculus 2 Trigonometric Substitution - I'm working this problem: ∫ [1-tan...
- Precalculus/Trig - I can't seem to prove these trig identities and would really ...
- precal - 1/tanx-secx+ 1/tanx+secx=-2tanx so this is what I did: =tanx+secx+tanx-...
- Pre-Calculus - 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...
- Trig - If secx = 8 and -pi/2 < x < 0, find the exact value of sin2x Use ...
- Pre-Calculus - How can this identity be proved/verified? cscx-sinx=1/(secxtanx) ...
- Calculus - Q: If y=sinx/(1+tanx), find value of x not greater than pi, ...

More Related Questions