Find the exact value of each trigonometric function for the given angle θ.
(2, -sqrt(5) ), cotθ
w/ unit cirlce
line in 4th quad
cot(θ) = -2/sqrt(5)
The triangle is in the fourth quadrant, so you can create a triangle which has the hypotenuse as 3, leg1 as 2, and leg2 as sqrt(5). However, keep in mind that when you for cotangent (adjacent/opposite), you put in a negative sign, because the original given point is negative and in the fourth quadrant.
Ty Ms. C
To find the value of cotθ for the given point (2, -√5) in the fourth quadrant, we can use the unit circle.
1. First, let's determine the values of sinθ and cosθ using the coordinates of the point (2, -√5). The x-coordinate represents cosθ, while the y-coordinate represents sinθ in the unit circle.
The x-coordinate is 2, so cosθ = 2.
The y-coordinate is -√5, so sinθ = -√5.
2. Next, let's find the value of tanθ. Since tanθ is the ratio of sinθ to cosθ, we can calculate it as follows:
tanθ = sinθ / cosθ
tanθ = (-√5) / 2
3. Finally, we can obtain the value of cotθ by taking the reciprocal of tanθ:
cotθ = 1 / tanθ
cotθ = 1 / [(-√5) / 2]
cotθ = 2 / (-√5)
∴ cotθ = -2 / √5
Therefore, the exact value of cotθ for the given point (2, -√5) in the fourth quadrant on the unit circle is -2/√5.
To find the exact value of the cotangent function for the angle θ in the fourth quadrant, we need to use the unit circle and the given point (2, -√5).
1. Start by drawing the unit circle, which is a circle with a radius of 1 centered at the origin (0, 0). Divide the circle into four quadrants.
2. Locate the point (2, -√5) in the fourth quadrant. This means that the x-coordinate is positive (2) and the y-coordinate is negative (-√5).
3. Draw a line from the origin (0, 0) to the point (2, -√5). This line represents the hypotenuse of a right triangle.
4. Now, we can determine the lengths of the other two sides of the right triangle. The horizontal side, adjacent to the angle θ, corresponds to the x-coordinate (2). The vertical side, opposite to the angle θ, corresponds to the y-coordinate (-√5).
5. In the fourth quadrant, the cotangent function is defined as the ratio of the adjacent side to the opposite side. So, cotθ = adj/op = 2/(-√5).
6. Simplify the value by multiplying both the numerator and the denominator by √5, to eliminate the square root in the denominator:
cotθ = 2/(-√5) * (√5/√5) = -2√5/5.
Therefore, the exact value of cotθ for the given angle θ, when represented by the point (2, -√5) in the unit circle, is -2√5/5.