if sinx=(4/5), where 0 degrees<x<90 degrees, find the value of cos (x+180)
25+25+100+n=250
since x is in the first quadrant, then x+180º is in the third quadrant, and cos(x+180) = =cos x
You should recognize the 3,4,5 right-angled triangle and cosx = 3/5
so cos(x+180)=-3/5
3x+y=90+2x+y=90
To find the value of cos(x+180), we need to determine the value of cos(x).
Given that sin(x) = 4/5, we can use the Pythagorean identity to find cos(x).
The Pythagorean identity states that sin^2(x) + cos^2(x) = 1.
Since sin(x) = 4/5, we can substitute this value into the equation:
(4/5)^2 + cos^2(x) = 1
Simplifying, we have:
16/25 + cos^2(x) = 1
To isolate cos^2(x), we subtract 16/25 from both sides of the equation:
cos^2(x) = 1 - 16/25
cos^2(x) = 25/25 - 16/25
cos^2(x) = 9/25
Taking the square root of both sides, we find:
cos(x) = sqrt(9/25)
cos(x) = 3/5
Since x is in the first quadrant, x + 180 degrees is in the third quadrant. In the third quadrant, the cosine function has a negative value.
Therefore, cos(x+180) = -cos(x) = -3/5.