If angle X is an acute angle with sinX=3/5, what is the value of secX?
45
52
53
54
given that sinX=3/5 and knowing that sinx = opposite/hypotenuse or y/r
we know from x^2 + y^2 = r^2
x^2 + 3^2 = 5^2
x^2 = 16
x = +4, since you said x was acute
since sec x = 1/cosx = 1/(4/5) = 5/4
all given answers are incorrect, it looks they could be choices for angles
but even that is wrong, since X would be appr 37°
that's because M doesn't know how to include a virgule in fractions.
I think choice D was meant to be 5/4
To find the value of secX, we need to use the relationship between sine (sin) and secant (sec) functions.
The relationship between sine and secant is as follows:
secX = 1 / cosX
To find cosX, we can use the Pythagorean identity, which states:
sin^2(X) + cos^2(X) = 1
Given that sinX = 3/5, we can substitute this value into the Pythagorean identity equation:
(3/5)^2 + cos^2(X) = 1
Simplifying the equation, we have:
9/25 + cos^2(X) = 1
To solve for cos^2(X), we subtract 9/25 from both sides:
cos^2(X) = 1 - 9/25
cos^2(X) = 16/25
Taking the square root of both sides, we find:
cosX = ± √(16/25)
Since angle X is an acute angle, cosX is positive. So we have:
cosX = √(16/25)
cosX = 4/5
Now, we can calculate secX using the relationship secX = 1 / cosX:
secX = 1 / (4/5)
secX = 5/4
Therefore, the value of secX is 5/4.
To find the value of secX, we need to use the relationship between sine (sin) and secant (sec) functions. The sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
We are given that sinX = 3/5, which means that the side opposite angle X has a length of 3 units and the hypotenuse has a length of 5 units. We can use the Pythagorean theorem to find the length of the adjacent side.
By Pythagorean theorem:
(Adjacent side)^2 + (Opposite side)^2 = (Hypotenuse)^2
Let's call the adjacent side "a."
a^2 + 3^2 = 5^2
a^2 + 9 = 25
a^2 = 16
a = ±4
Since angle X is an acute angle, the adjacent side should be positive. Therefore, the value of the adjacent side is 4 units.
Now that we have the values of the adjacent side and the hypotenuse, we can find the value of secX. The secant function is the reciprocal of the cosine function.
cosX = adjacent side / hypotenuse
cosX = 4/5
secX = 1 / cosX
secX = 1 / (4/5)
secX = 5/4
Therefore, the value of secX is 5/4.
None of the provided options (45, 52, 53, 54) are equal to 5/4. So, none of the provided options is the correct answer.