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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) = 
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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.

This problem has been solved

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