To find sin(t), cos(t), and tan(t) for the given terminal point P(x,y) = (-2/5, 21/5), we can use the definition of these trigonometric functions in relation to the coordinates of the terminal point on the unit circle.
Let r be the radius of the unit circle, which is always 1.
Using the Pythagorean theorem, we can find the value of r by:
r^2 = x^2 + y^2
r^2 = (-2/5)^2 + (21/5)^2
r^2 = 4/25 + 441/25
r^2 = 445/25
r = sqrt(445)/5
Now, we can find sin(t) and cos(t) using the coordinates x and y:
sin(t) = y / r
sin(t) = (21/5) / (sqrt(445)/5)
sin(t) = 21 / sqrt(445)
cos(t) = x / r
cos(t) = (-2/5) / (sqrt(445)/5)
cos(t) = -2 / sqrt(445)
Finally, we can find tan(t) using the definition:
tan(t) = sin(t) / cos(t)
tan(t) = (21 / sqrt(445)) / (-2 / sqrt(445))
tan(t) = -21 / 2
Therefore, for the given terminal point P(x,y) = (-2/5, 21/5), we have:
sin(t) = 21 / sqrt(445)
cos(t) = -2 / sqrt(445)
tan(t) = -21 / 2
To find sin(t),cos(t)and tan(t) for the given terminal point p(x,y)=(-2/5,21/5) we can use the definition of these trignometric functions in relation to the coordinates of the terminal point on the unit circle
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