Question #18d08

2 Answers
Aug 8, 2017

Answer:

#cosA=+-(2sqrt2)/3#

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.

Aug 8, 2017

Answer:

#cosA = +-(2sqrt2)/3#

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 #sin#, we know that the ratio gives us

  • #"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.