The point (5,-2) in on the terminal side of an angle t. Find cos
Did you mean,
find cos t ?
if so,
cos t = 5/√29
To find the cosine of angle t, we need to evaluate the x-coordinate of the point (5, -2) and divide it by the length of the line segment from the origin to the point.
Here's how to do it step by step:
1. Recall the definition of cosine:
cos(t) = adjacent / hypotenuse
2. Determine the adjacent side:
In this case, the adjacent side is the x-coordinate of the point (5, -2), which is 5.
3. Calculate the hypotenuse:
The hypotenuse is the length of the line segment from the origin to the point. To find it, we can use the Pythagorean theorem.
The distance from the origin to (5, -2) is the square root of the sum of the squares of its coordinates:
hypotenuse = √(5^2 + (-2)^2) = √(25 + 4) = √29
4. Substitute the values into the cosine formula:
cos(t) = adjacent / hypotenuse = 5 / √29
5. Simplify the expression:
To simplify the expression, multiply the numerator and the denominator by √29:
cos(t) = (5 * √29) / (√29 * √29) = (5 * √29) / 29
Therefore, the cosine of angle t is (5 * √29) / 29.
To find the value of cosine (cos) for the given point (5, -2) on the terminal side of an angle t, we need to calculate the ratio of the x-coordinate to the magnitude of the point:
cos(t) = x / r
where x is the x-coordinate of the point, and r is the magnitude of the point.
In this case, the x-coordinate of the point (5, -2) is 5. To find the magnitude of the point, we can use the Pythagorean theorem:
r = sqrt((x^2) + (y^2))
where y is the y-coordinate of the point.
In this case, the y-coordinate of the point (5, -2) is -2. Plugging these values into the equation, we have:
r = sqrt((5^2) + (-2^2))
= sqrt(25 + 4)
= sqrt(29)
Now, we can calculate the cosine value:
cos(t) = x / r
= 5 / sqrt(29)
So, the value of cos(t) for the given point is 5 / sqrt(29).