trigonometric functions state that cosine functions are even so that automatically rules out the first two options.
sine functions are odd so the last two are right.
odd functions: f(-x)=-f(x)
so the sine would be: sin(-x)=-sin(x)
the third option should be the right answer
Answer
given,
side of rectangle, AB = CD = 32
BC = DA = 24
rectangle is rotated 90° clockwise about C.
then rotated 90° clockwise about D.
Path traveled by the point A for first rotation will be in circle with radius AC.
AC = 40
θ₁ = 90°
D₁ = 1256.64
For the second rotation Point A will move in circular path with radius of AD
AD = 24
θ₁ = 90°
D₂ = 452.39
total path traveled by the point A
D = D₁ + D₂
D = 1256.64 + 452.39
D = 1709.03
Answer:
38
Step-by-step explanation:
AB is parallel to CD. So, <ABC = <BCD.
Now, <BCD = <ABC = 180 - 111 - 31 = 38
Let
rR--------> radius of the circle R
rS-------> radius of the circle S
LR------> the length of the intercepted arc for circle R
LS------> the length of the intercepted arc for circle S
we have that
rR=2/3 ft
rS=3/4 ft
rR/rS=8/9--------> rS/rR=9/8
LR=(4/9)π ft
we know that
if Both circle R and circle S have a central angle , the ratio of the radius of circle R to the radius of circle S is equals to the ratio of the length of circle R to the length of circle S
rR/rS=LR/LS--------> LS=LR*rS/rR-----> [(4/9)π*9/8]----> (1/2)π ft
the answer is
the length of the intercepted arc for circle S is (1/2)π ft
The area of a circle is given by
whereas the circumference is given by
If we want these two values to be (numerically) the same we have to set and solve for the radius:
So, one (trivial) solution is . A circle with radius 0 is just a point, and so both area and circumference are zero.
The other solution is . In fact, you have