The point (-5/12) is on the terminal side of an angle theta in standard position. Find Sin theta, cos theta and tan theta Thank You!
To find the values of sin(theta), cos(theta), and tan(theta) for an angle in standard position, we need to use the coordinates of the point on the terminal side of the angle.
In this case, the point is (-5/12).
First, let's find the hypotenuse of the right triangle formed by the point (-5/12). The hypotenuse is the distance from the origin (0,0) to the point (-5/12). We can use the Pythagorean theorem to find this distance.
The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In our case, the hypotenuse is the distance, and the two sides are the x-coordinate (-5/12) and the y-coordinate (0).
Therefore, the hypotenuse can be calculated as follows:
hypotenuse = sqrt((-5/12)^2 + 0^2)
Calculating this, we get:
hypotenuse = sqrt(25/144)
hypotenuse = 5/12
Now, we can find the values of sin(theta), cos(theta), and tan(theta) using the following formulas:
sin(theta) = y-coordinate / hypotenuse
cos(theta) = x-coordinate / hypotenuse
tan(theta) = y-coordinate / x-coordinate
Given that the y-coordinate is 0 and the x-coordinate is -5/12, we can plug these values into the respective formulas:
sin(theta) = 0 / (5/12)
sin(theta) = 0
cos(theta) = (-5/12) / (5/12)
cos(theta) = -5/12 ÷ 5/12
cos(theta) = -1
tan(theta) = 0 / (-5/12)
tan(theta) = 0
Therefore, sin(theta) = 0, cos(theta) = -1, and tan(theta) = 0.
Note: In standard position, angles have a positive x-axis direction as the initial side, and theta is measured counterclockwise from the positive x-axis.