Elliana is planting flowers in her rectangular backyard. The backyard is 7 yards long and 8 yards wide. Elliana wants to plant s
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The equation of the polar curve is an even cosine function.
In geometry, polar curves are curves that are represented by the polar coordinates such that they are drawn around a fixed point
The equation of the polar curve is given as:
To graph the polar curve, we make use of the following representations:
- r represents the y-axis
represents the x-axis
Using the above representation, we can graph the polar curve
See attachment for the graph that represents
Read more about polar curves at:
Let's start with the drawing. (See the drawing at the bottom of this answer.)
Draw a vertical segment.
At the bottom endpoint, draw a horizontal segment to the right.
The angle at the bottom left is a right angle.
So far this should look like an "L" shape.
The vertical segment is the wall, and the horizontal segment is the ground.
Now draw a segment that connects the right endpoint of the horizontal segment and the top endpoint of the vertical segment. Now you have a right triangle. The diagonal segment represents the ladder. The diagonal segment is the hypotenuse. Label the diagonal segment, the hypotenuse, 12 ft.
Label the vertical segment, the wall, 11.8 ft.
The angle at the bottom right is A. It is the angle the ladder makes with the ground. This angle cannot be greater than 75 degrees.
Now we use trigonometry to find the measure of angle A.
For this right triangle, and its angle A, you have a hypotenuse that measures 12 ft, and an opposite leg that measures 11.8 ft.
We need to find angle A.
The trig ratio that relates the opposite leg and the hypotenuse is the sine.
Since the sine of angle A equals 0.98333, we use the inverse sine function to find the measure of angle A.
Answer:
The angle the ladder makes with the ground is 79.5 degrees which is greater than 75 degrees, so the ladder it will be unsafe in this position.
|\
| \
| \
| \
opp = | \ hyp = 12
= 11.8 | \
| \
|_______\ A
Draw a vertical segment.
At the bottom endpoint, draw a horizontal segment to the right.
The angle at the bottom left is a right angle.
So far this should look like an "L" shape.
The vertical segment is the wall, and the horizontal segment is the ground.
Now draw a segment that connects the right endpoint of the horizontal segment and the top endpoint of the vertical segment. Now you have a right triangle. The diagonal segment represents the ladder. The diagonal segment is the hypotenuse. Label the diagonal segment, the hypotenuse, 12 ft.
Label the vertical segment, the wall, 11.8 ft.
The angle at the bottom right is A. It is the angle the ladder makes with the ground. This angle cannot be greater than 75 degrees.
Now we use trigonometry to find the measure of angle A.
For this right triangle, and its angle A, you have a hypotenuse that measures 12 ft, and an opposite leg that measures 11.8 ft.
We need to find angle A.
The trig ratio that relates the opposite leg and the hypotenuse is the sine.
Since the sine of angle A equals 0.98333, we use the inverse sine function to find the measure of angle A.
Answer:
The angle the ladder makes with the ground is 79.5 degrees which is greater than 75 degrees, so the ladder it will be unsafe in this position.
|\
| \
| \
| \
opp = | \ hyp = 12
= 11.8 | \
| \
|_______\ A