The given point, (2,0) lies on the terminal side of an angle X in standard position. What are the six trigonometric functions of X?
well, the point lies on the x-axis, so X = 0
Surely you can handle the trig functions of 0 ...?
To find the trigonometric functions of angle X, we need to determine the values of the six trigonometric ratios (sine, cosine, tangent, cosecant, secant, and cotangent) for angle X.
Step 1: Determine the values of x and y coordinates of the given point.
Given point: (2, 0)
The x-coordinate represents the adjacent side, and the y-coordinate represents the opposite side.
So, x = 2 and y = 0.
Step 2: Determine the hypotenuse.
Using the Pythagorean theorem, we can calculate the hypotenuse of the right triangle formed.
Hypotenuse (h) = √(adjacent^2 + opposite^2)
h = √(2^2 + 0^2)
= √4
= 2
Step 3: Calculate the values of the six trigonometric functions.
sine (sin) = opposite/hypotenuse
= y/h
= 0/2
= 0
cosine (cos) = adjacent/hypotenuse
= x/h
= 2/2
= 1
tangent (tan) = opposite/adjacent
= y/x
= 0/2
= 0
cosecant (csc) = 1/sin
= 1/0 (undefined)
secant (sec) = 1/cos
= 1/1
= 1
cotangent (cot) = 1/tan
= 1/0 (undefined)
The six trigonometric functions of angle X are:
sin(X) = 0
cos(X) = 1
tan(X) = 0
csc(X) = undefined
sec(X) = 1
cot(X) = undefined
To find the six trigonometric functions of angle X in standard position, we first need to determine the values of the adjacent, opposite, and hypotenuse sides of the right triangle formed by the point (2,0).
Since the given point (2,0) lies on the x-axis, the adjacent side is the x-coordinate, which is 2. The opposite side is the y-coordinate, which is 0. And the hypotenuse, which is the distance from the origin to the given point, can be found using the Pythagorean theorem.
Pythagorean theorem: hypotenuse^2 = adjacent^2 + opposite^2
In this case, the hypotenuse^2 = 2^2 + 0^2 = 4, so the hypotenuse is √4 = 2.
Now we can calculate the six trigonometric functions.
1. Sine (sin): sin(X) = opposite/hypotenuse = 0/2 = 0
2. Cosine (cos): cos(X) = adjacent/hypotenuse = 2/2 = 1
3. Tangent (tan): tan(X) = opposite/adjacent = 0/2 = 0
4. Cosecant (csc): csc(X) = 1/sin(X) = undefined (since sin(X) = 0)
5. Secant (sec): sec(X) = 1/cos(X) = 1/1 = 1
6. Cotangent (cot): cot(X) = 1/tan(X) = undefined (since tan(X) = 0)
Therefore, the six trigonometric functions of angle X in standard position are:
sin(X) = 0
cos(X) = 1
tan(X) = 0
csc(X) = undefined
sec(X) = 1
cot(X) = undefined