The point (-3, 4) is on the terminal side of angle θ in standard position. Find
cot θ.
for (-3,4)
x = -3, y = 4
cotØ = x/y = - 3/4
Well, if (-3, 4) is on the terminal side of angle θ, it means we're dealing with a right triangle. So let's find the values we need. The length of the adjacent side is -3 (because it's negative, it probably had a fight with the positive side), and the length of the opposite side is 4. Now, to find cot θ, we use the formula cot θ = adjacent side / opposite side. Plug in the values we found, and we get -3/4. And voila! cot θ = -3/4, which means the angle θ likes to be a little negative and a little irrational.
To find cot θ, we need to first find the value of tan θ.
The point (-3, 4) is on the terminal side of θ, which means that the side opposite to the angle θ is 4 and the side adjacent to the angle θ is -3 (since the point is in the third quadrant).
We know that tan θ is equal to the ratio of the side opposite to the angle θ to the side adjacent to the angle θ:
tan θ = opposite / adjacent
= 4 / -3
= -4/3
To find cot θ, we can take the reciprocal of tan θ:
cot θ = 1 / tan θ
= 1 / (-4/3)
= -3/4
Therefore, the value of cot θ is -3/4.
To find cot θ, we need to find the value of θ first.
In standard position, the point (-3, 4) is on the terminal side of angle θ.
Let's draw a right triangle with the given point as one of the vertices:
|
| θ
-----
| /
| /
| /
-----
| (-3, 4)
The side adjacent to θ is the x-coordinate of the point, which is -3, and the side opposite to θ is the y-coordinate of the point, which is 4.
Now, we can use the tangent function to find θ.
tan θ = opposite/adjacent
tan θ = 4/-3
Using inverse tangent (arctan) on both sides, we can find θ:
θ = arctan (4/-3)
Now that we have found θ, we can find the cotangent.
cot θ is equal to the reciprocal of the tangent:
cot θ = 1/tan θ
So, cot θ = 1/tan(arctan (4/-3)).