x=−sint,y=cost,0≤t≤π  draw currve 

Here is the plot of the curve for \( x = -\sin t \) and \( y = \cos t \) over the interval \( 0 \leq t \leq \pi \). The curve traces a half-circle on the left side of the unit circle, starting at \( (0, 1) \) and ending at \( (0, -1) \).

Would you like a step-by-step explanation of the drawing process or have any questions?

Here are some related questions:
1. How do parametric equations define curves in the plane?
2. What happens if we change the range of \( t \) beyond \( [0, \pi] \)?
3. How would the curve change if we used \( x = \sin t \) and \( y = \cos t \) instead?
4. How can we derive the equation of this curve in Cartesian form?
5. What types of shapes can be created using trigonometric functions in parametric equations?

**Tip:** When working with parametric equations, try plotting sample points to get a sense of the curve’s direction and shape.

x = -sin(t), y = cos(t), 0 ≤ t ≤ π; draw curve

Explore the parametric curve defined by x = -sin(t) and y = cos(t) over the interval 0 ≤ t ≤ π. This example demonstrates the use of trigonometric functions in parametric equations to create a half-circle on the unit circle's left side. Ideal for students in Grades 10-12 learning about curve plotting and parametric equations.

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