The terminal point P(x, y) determined by a real number t is given. Find sin(t), cos(t), and tan(t).1161, − 6061sin(t) = −6061 cos(t) = 1161 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).1161, − 6061sin(t) = −6061 cos(t) = 1161 tan(t) =
Solution
To find sin(t), cos(t), and tan(t), we first need to find the radius r using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c²
Here, x and y are the coordinates of the point P, so we can consider them as the two sides of a right triangle. Therefore, we can calculate r (the hypotenuse) as follows:
r = sqrt(x² + y²) r = sqrt((1161)² + (-6061)²) r = sqrt(1348921 + 36757921) r = sqrt(38106842) r = 6173.4
Now, we can find sin(t), cos(t), and tan(t) as follows:
sin(t) = y/r = -6061/6173.4 = -0.9818 cos(t) = x/r = 1161/6173.4 = 0.1881 tan(t) = y/x = -6061/1161 = -5.2205
So, sin(t) = -0.9818, cos(t) = 0.1881, and tan(t) = -5.2205.
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