Question #18d08
2 Answers
Answer:
Explanation:
#•color(white)(x)sin^2x+cos^2x=1#
#rArrcosx=+sqrt(1sin^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.
Answer:
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.