- #1
majormuss
- 124
- 4
Homework Statement
How do I solve this trig question?
cot(Arctan (-√(5)/2))
Homework Equations
The usual equation I know of which is easy o identify on the Unit circle is √3/2. I don't know how to approach this one..
The value of cot(Arctan (-√(5)/2)) is equal to -2/√(5).
To solve cot(Arctan (-√(5)/2)), we can use the identity cot(x) = cos(x)/sin(x). By substituting -√(5)/2 for x in the identity, we get cos(Arctan (-√(5)/2))/sin(Arctan (-√(5)/2)). Then, we can use the right triangle with sides -√(5), 2, and √(5) to find the values of cosine and sine, giving us -2/√(5) for cot(Arctan (-√(5)/2)).
The triangle in the question has sides -√(5), 2, and √(5), and the angle in question is the angle opposite the side -√(5). The value of cot(Arctan (-√(5)/2)) is equal to the adjacent side (2) divided by the opposite side (-√(5)), which is the same as the tangent of the angle in the triangle.
Yes, the value of cot(Arctan (-√(5)/2)) can be simplified further by rationalizing the denominator. By multiplying both the numerator and denominator by √(5), we get (-2√(5))/5, which is a simplified form of the original value.
The solution to cot(Arctan (-√(5)/2)) can be applied in real-life situations involving right triangles with sides -√(5), 2, and √(5). For example, if we know the length of the adjacent side and the angle opposite that side, we can use the value of cot(Arctan (-√(5)/2)) to find the length of the opposite side.