Find secx if sinx = -4/5 and 270 < x < 360.
tan^2x+1=sec^2x
(-4/5)^2+1=sec^2x
16/25+1=sec^2x
17/25=sec^2x
sqrt 17/5
I don't know if it should be positive or negative.
You are in the fourth quadrant
the secant has the same sign as the cosine, and in the fourth quadrant the cosine is positive,
Your answer is not correct
Here is an easier way than trying to use the formula you tried.
sinß = y/r = -4/5
so x^2 + (-4)^2 = 5^2
x = ±3 but you are in the fourth quadr, so x=+3
sec x = 1/cosx = 1/(3/5) = 5/3
To find sec(x), given that sin(x) = -4/5 and 270 < x < 360, you can use the identity:
sec^2(x) = 1 + tan^2(x)
First, find the value of tan(x):
Since sin(x) = -4/5, we can use the Pythagorean identity: sin^2(x) + cos^2(x) = 1
(-4/5)^2 + cos^2(x) = 1
16/25 + cos^2(x) = 1
cos^2(x) = 25/25 - 16/25
cos^2(x) = 9/25
cos(x) = ± √(9/25)
cos(x) = ± 3/5
Since 270 < x < 360, we know that x is in the fourth quadrant, where cos(x) is positive. Therefore, cos(x) = 3/5.
Now, use the identity tan(x) = sin(x)/cos(x) to find the value of tan(x):
tan(x) = sin(x)/cos(x)
tan(x) = (-4/5)/(3/5)
tan(x) = -4/3
Now you can substitute this value of tan(x) into the given identity:
sec^2(x) = 1 + tan^2(x)
sec^2(x) = 1 + (-4/3)^2
sec^2(x) = 1 + 16/9
sec^2(x) = 25/9
Taking the square root of both sides gives:
sec(x) = ± √(25/9)
sec(x) = ± (5/3)
However, since x is in the fourth quadrant where sec(x) is positive, we can conclude that sec(x) = 5/3.