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Math  /  Calculus

Questionhomework4.8: Problem 4 (1 point)
Find an equation of the tangent line to the curve x=sin⁡(5t),y=sin⁡(6t)x=\sin (5 t), \quad y=\sin (6 t) at t=πt=\pi. x(t)=□y(t)=□\begin{array}{l} x(t)=\square \\ y(t)=\square \end{array} (Note that because the correctness of a parametrically described line depends on both x(t)x(t) and y(t)y(t), both of your answers may be marked incorrect if there is an error in one of them.)
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Studdy Solution
Use the point-slope form to find the equation of the tangent line:
The point-slope form is y−y1=m(x−x1) y - y_1 = m(x - x_1) .
Substitute m=−65 m = -\frac{6}{5} , x1=0 x_1 = 0 , and y1=0 y_1 = 0 :
y−0=−65(x−0) y - 0 = -\frac{6}{5}(x - 0) y=−65x y = -\frac{6}{5}x
The equation of the tangent line is:
y=−65x \boxed{y = -\frac{6}{5}x}

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