Which statement describes the graph and orientation of the parametric equations x=9cost and y=9sint?
A.The graph is a circle with a radius of 3. The orientation is counterclockwise as t increases.
B. The graph is a circle with a radius of 9. The orientation is clockwise as t increases.
C. The graph is a circle with a radius of 3. The orientation is clockwise as t increases.
D. The graph is a circle with a radius of 9. The orientation is counterclockwise as t increases.
@ ooblek. I appreciate your assistance. How did you get x^2+y^2=9 from the problem?
D. The graph is a circle with a radius of 9. The orientation is counterclockwise as t increases.
Just like a clown spinning hoops in the circus, the graph of these parametric equations creates a circle with a radius of 9. And just like the clown's wacky routine, the orientation of the circle is counterclockwise as t increases. So remember, when it comes to this graph, it's all about the big rings and silly rotations!
To determine the graph and orientation of the given parametric equations, x = 9cos(t) and y = 9sin(t), we can analyze the equation and properties of trigonometric functions.
The general equations for a circle in parametric form are x = a + rcos(t) and y = b + rsin(t), where (a, b) is the center of the circle, r is the radius, and t is the angle.
In this case, we have x = 9cos(t) and y = 9sin(t). Based on these equations, we can observe that the center of the circle is (0, 0) since there are no constants added to the trigonometric functions.
The radius of the circle can be determined by inspecting the coefficients of cos(t) and sin(t) in the parametric equations. In this case, the coefficient for both cos(t) and sin(t) is 9, indicating that the radius is 9.
Now, let's determine the orientation of the graph. When t increases, the angle in the trigonometric functions increases. In trigonometry, we know that the angles in the unit circle increase in a counterclockwise manner. Therefore, as t increases, the graph of the parametric equations would also rotate counterclockwise.
Putting all the information together, we can conclude that the correct statement is:
A. The graph is a circle with a radius of 9. The orientation is counterclockwise as t increases.
note that x^2+y^2 = 9
now review how angles are graphed in polar coordinates.