. The psychology club is having a self-proclaimed psychic come to their campus fund-raising event to demonstrate his abilities.
1 answer:
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Answer:
On a unit circle, the point that corresponds to an angle of is at position
.
The point that corresponds to an angle of is at position
.
Step-by-step explanation:
On a cartesian plane, a unit circle is
- a circle of radius
,
- centered at the origin
.
The circle crosses the x- and y-axis at four points:
,
,
, and
.
Join a point on the circle with the origin using a segment. The "angle" here likely refers to the counter-clockwise angle between the positive x-axis and that segment.
When the angle is equal to , the segment overlaps with the positive x-axis. The point is on both the circle and the positive x-axis. Its coordinates would be
.
To locate the point with a angle, rotate the
segment counter-clockwise by
. The segment would land on the positive y-axis. In other words, the
-point would be at the intersection of the positive y-axis and the circle. Its coordinates would be
.
Answer:
- quadratic function
- y-intercept: y = -6
- x-intercepts: x = 2 and x = 6
- y = 2, x = 4
- y ≥ 0
Step-by-step explanation:
The given graph is a <u>parabola</u> and so it a quadratic function.
The y-intercept is the point at which the curve <u>crosses the y-axis</u>.
From inspection of the graph, this is when y = -6.
The x-intercepts are the points at which the curve <u>crosses the x-axis</u>.
From inspection of the graph, the x-intercepts are x = 2 and x = 6.
The vertex is the <u>turning point</u> of the graph, so the <u>minimum point</u> of a parabola that opens <u>upwards</u>, and the <u>maximum</u> point of a parabola that opens <u>downwards</u>.
From inspection of the graph, the vertex is at (4, 2), so the greatest value of y is y = 2, and it occurs when x = 4.
The curve is <u>above the x-axis</u> between the interval x = 2 and x = 6.
Therefore, the function value is equal to zero or <u>positive</u> in this interval.
So the function value in the given interval is y ≥ 0.
