The point (7,2) determines a poistion angle "t". Find the exact value of sin(t).
To find the exact value of sin(t), we first need to determine the trigonometric function values based on the coordinates of the point (7,2).
To do this, we can use the formulas for the trigonometric functions given the x and y coordinates. In this case, we will use the sine function, sin(t), which is defined as the ratio of the opposite side to the hypotenuse in a right triangle.
First, let's plot the point (7,2) on a Cartesian plane:
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| ● (7,2)
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Next, we can draw a right triangle with one of the sides coinciding with the positive x-axis and the hypotenuse connecting the origin (0,0) to the point (7,2).
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| ● (7,2)
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|_______|______|_______
Using the coordinates, we can determine the length of the opposite side and the hypotenuse:
The opposite side (y-coordinate): 2
The hypotenuse: SQRT((x-coordinate)^2 + (y-coordinate)^2)
= SQRT(7^2 + 2^2)
= SQRT(49 + 4)
= SQRT(53)
Now, we can use the formula sin(t) = opposite/hypotenuse, where t is the position angle:
sin(t) = 2/SQRT(53)
Therefore, the exact value of sin(t) for the position angle determined by the point (7,2) is 2/SQRT(53).