If sin x = -12/13 and tan x is positive, find the values of cos x and tan x ?
Thanks!
Thanks!
2 Answers
Determine the Quadrant first
Explanation:
Since
Since
In Quadrant III, cosine is also negative.
Draw a triangle in Quadrant III as indicated. Since
By the Pythagorean Theorem, the length of the adjacent side is
However, since we are in Quadrant III, the 5 is negative. Write -5.
Now use the fact that
and
Explanation:
#"using the "color(blue)"trigonometric identity"#
#•color(white)(x)sin^2x+cos^2x=1#
#rArrcosx=+-sqrt(1-sin^2x)#
#"since "sinx<0" and "tanx>0#
#"then x is in the third quadrant where "cosx<0#
#rArrcosx=-sqrt(1-(-12/13)^2)#
#color(white)(rArrcosx)=-sqrt(25/169)=-5/13#
#tanx=sinx/cosx=(-12/13)/(-5/13)=-12/13xx-13/5=12/5#