SOLUTION: allen111@purdue.edu {{{Sec(theta)=-1.5}}} {{{pi/2<theta<pi}}} Find the remaining 5 trigonometric ratios for {{{theta}}}

Algebra ->  Trigonometry-basics -> SOLUTION: allen111@purdue.edu {{{Sec(theta)=-1.5}}} {{{pi/2<theta<pi}}} Find the remaining 5 trigonometric ratios for {{{theta}}}      Log On


   



Question 340529: allen111@purdue.edu
Sec%28theta%29=-1.5 pi%2F2%3Ctheta%3Cpi
Find the remaining 5 trigonometric ratios for theta

Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!
Sec%28theta%29=-1.5 pi%2F2%3Ctheta%3Cpi
Find the remaining 5 trigonometric ratios for q

We change -1.5 to the fraction -3%2F2

Since Sec%28theta%29=-3%2F2 we draw q in Quadrant II
and since Sec%28theta%29=r%2Fx we label the value of r as 3,
the numerator of -3%2F2, considering it as 3%2F%28-2%29,
and we label the value of x as the denominator -2.



Then we calculate the value of y by the Pythagorean relation:

x%5E2%2By%5E2=r%5E2
%28-2%29%5E2%2By%5E2=3%5E2
4%2By%5E2=9
y%5E2=5
y=sqrt%285%29

So we now label y as sqrt%285%29



Now the trig functions for q are:

sin%28theta%29=y%2Fr=sqrt%285%29%2F3

cos%28theta%29=x%2Fr=%28-2%29%2F3=-2%2F3

tan%28theta%29=y%2Fx=sqrt%285%29%2F-2=-sqrt%285%29%2F2



sec%28theta%29=r%2Fx=3%2F%28-2%29=-3%2F2%28given%29



Edwin