Question #18d08
2 Answers
Explanation:
#•color(white)(x)sin^2x+cos^2x=1#
#rArrcosx=+-sqrt(1-sin^2x)#
#rArrcosA=+-sqrt(1-(1/3)^2)#
#color(white)(rArrcosA)=+-sqrt(8/9)#
#color(white)(rArrcosA)=+-(2sqrt2)/3#
#"the sign of "cosA"# will be dependent on which quadrant A is in.
Explanation:
The sine of a right triangle is the ratio of the lengths opposite side to the hypotenuse, and the cosine is the ratio of the adjacent side to the hypotenuse.
From the given
-
#"opposite" = 1# -
#"hypotenuse" = 3#
We can use the Pythagorean theorem to find the length of the adjacent side:
#"adjacent" = sqrt(3^2 - 1^2) = color(red)(ul(+-2sqrt2#
And since
#cos = "adjacent"/"hypotenuse"#
We have
#color(blue)(ulbar(|stackrel(" ")(" "cos = +-(2sqrt2)/3" ")|)#
depending on the quadrant it lies in.
