# Trig

If secx = 8 and -pi/2 < x < 0, find the exact value of sin2x

Use the identity sin 2x = 2(sinx)(cosx)

if secx = 8, then cosx = 1/8 where x is in the fourth quadrant.
consider a right angled triangle with x=1, r=8, then y=??
by Pythagoras 1^2 + y^2 = 8^2
y = -√63 (it has to be negative in IV)
so sinx = -√63/8

so we have sin 2x = 2(-√63/8)(1/8)
=-√63/32

1. 👍 0
2. 👎 0
3. 👁 177

## Similar Questions

1. ### pre-cal

find all solutions in interval [0,2pi] tan²x = -3/2 secx This question may look tricky, but its actually quite simple. First: rearrange the pythagorean identity tan²x+1=sin²x so that it reads tan²x=sin²x-1 Then replace the

asked by ethan on May 16, 2007
2. ### trig

How do I find the exact value of sin2x when secx is equal to the negative square root of three

asked by Cody on February 18, 2011
3. ### trig

secx = 4 in Q2 find sin2x,cos2x,tan2x

asked by j on October 30, 2017
4. ### Pre-Calc Help!!!!!!!!

1+sin2x/sin2x=1+1/2(secx)(cscx)

asked by Amanda on April 19, 2012
5. ### math

I have to find an exact solutions on the interval [0,pi) for both of these problems-- 1) 2sin2x = sqrtx and 2) 1-2sqrt2 sinxcosx = 0 I know this much: 1) sin2x = (sqrt x)/2 = 2sinxcosx = (sqrt x)/2 What do I need to do next? 2)

asked by kristie on August 1, 2006

Which of the following are identities? Check all that apply. (Points : 2) sin2x = 1 - cos2x sin2x - cos2x = 1 tan2x = 1 + sec2x cot2x = csc2x - 1 Question 4. 4. Which of the following equations are identities? Check all that

asked by Jane on January 12, 2014

Express sec2x in terms of tanx and secx I know you have to sec(2x) = 1/cos(2x) = 1/(cos²x - sin²x) But how do you split that. Like how to simplify that?

asked by Anonymous on November 2, 2016
8. ### Calculus

I need to find the exact solution to: 2sin2x = sqrt(x)on the interval (0,pi) This is how I started it, but I don't think it's correct. sin2x = sqrt(x)/2 2sinxcosx = sqrt(x)/2 sinxcosx = sqrt(x)/4 What do I need to do now? need to

asked by Jen on August 21, 2006
9. ### Precalc

Find the exact solutions to each equation for the interval [0,360) 2cosx-secx = 1

asked by Sean on December 6, 2007
10. ### Calculus

find the derivative y= csc^-1 (secx) 0 less than or equal to x less than or equal to 2¤Ð what did i do wrong? - 1/ secx sqrt(secx^2 -1) * secxtanx

asked by Jin on October 29, 2010

More Similar Questions