Length of a circumference=2πr
r=radius=6 feet.
lengt of this circumference=2π6 feet=12π feet.
1 circumference=360º; then:
360º-------------------12π feet
6º---------------------- x
360º * x=6º * 12π feet
x=(6º * 12π feet) / 360º=π/30 feet (≈0,105 feet).
Solution: π/30 feet
Answer:
x = {nπ -π/4, (4nπ -π)/16}
Step-by-step explanation:
It can be helpful to make use of the identities for angle sums and differences to rewrite the sum:
cos(3x) +sin(5x) = cos(4x -x) +sin(4x +x)
= cos(4x)cos(x) +sin(4x)sin(x) +sin(4x)cos(x) +cos(4x)sin(x)
= sin(x)(sin(4x) +cos(4x)) +cos(x)(sin(4x) +cos(4x))
= (sin(x) +cos(x))·(sin(4x) +cos(4x))
Each of the sums in this product is of the same form, so each can be simplified using the identity ...
sin(x) +cos(x) = √2·sin(x +π/4)
Then the given equation can be rewritten as ...
cos(3x) +sin(5x) = 0
2·sin(x +π/4)·sin(4x +π/4) = 0
Of course sin(x) = 0 for x = n·π, so these factors are zero when ...
sin(x +π/4) = 0 ⇒ x = nπ -π/4
sin(4x +π/4) = 0 ⇒ x = (nπ -π/4)/4 = (4nπ -π)/16
The solutions are ...
x ∈ {(n-1)π/4, (4n-1)π/16} . . . . . for any integer n
vbbbbbbbbbbbbbbbbbdnnnnnAnswer:
Step-by-step explanation:
Using relations in a right triangle, it is found that:
- Since x and y are complementary angles, we have that sin(xº) = cos(yº).
<h3>What are the relations in a right triangle?</h3>
The relations in a right triangle are given as follows:
- The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
- The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
- The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
The hypotenuse in this problem is given as follows:
h = 10.
The sine of x is:
The cosine of y is:
Since x and y are complementary angles, we have that sin(xº) = cos(yº).
More can be learned about relations in a right triangle at brainly.com/question/26396675
#SPJ1
18x - 16 = -12x - 4 ---> Add 12x to both sides
30x - 16 = -4 ---> Add 16 to both sides
30x = 12 ---> Divide both sides by 30
x = 0.4
