The terminal point P(x, y) determined by a real number t is given. Find sin(t), cos(t), and tan(t).1717, 41717sin(t) = cos(t) = tan(t) =
Question
The terminal point P(x, y) determined by a real number t is given. Find sin(t), cos(t), and tan(t).
1717, 41717
sin(t) =
cos(t) =
tan(t) =
Solution
The terminal point P(x, y) is given as (1717, 41717).
The value of t is determined by the angle that the line OP makes with the positive x-axis, where O is the origin.
In a unit circle, the x-coordinate represents cos(t) and the y-coordinate represents sin(t).
However, the given point is not on the unit circle. So, we need to find the radius r of the circle that the point lies on using the formula r = sqrt(x^2 + y^2).
r = sqrt((1717)^2 + (41717)^2) = sqrt(1745566890) = 41770
Now, we can find sin(t), cos(t), and tan(t) as follows:
sin(t) = y/r = 41717/41770 = 0.9987
cos(t) = x/r = 1717/41770 = 0.0411
tan(t) = y/x = 41717/1717 = 24.29
So, sin(t) = 0.9987, cos(t) = 0.0411, and tan(t) = 24.29.
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