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Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of dx at this point. x = sin t, y = cos t; t= - 4 Write the equation of the tangent line. y= x+ (Type exact answers, using radicals as needed.) What is the value of- dx at this point? dx (Type an exact answer, using radicals as needed.)Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of dx at this point. x= - cost, y = 2 + sint, t= The equation for the line tangent to the curve at t= s is y = (Simplify your answer. Type your answer in slope-intercept form.) dx (Simplify your answer.)Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y = g(t), find the slope of the curve x = f(t), y = g(t) at the given value of t. x= t* +t, y+ 31# =3x+12, t= 2 The slope of the curve at t = 2 is (Type an integer or a simplified fraction.)Find the length of the curve. (2t+ 1) 3/2 X= 3 , Osts 14 The length of the curve is (Simplify your answer.)Find the length of the curve. x = 8 sint- 8t cost, y = 8 cost+ 8t sint, Osts The length is units. (Type an exact answer, using It as needed.)