Answer:
sin(2x)=cos(π2−2x)
So:
cos(π2−2x)=cos(3x)
Now we know that cos(x)=cos(±x) because cosine is an even function. So we see that
(π2−2x)=±3x
i)
π2=5x
x=π10
ii)
π2=−x
x=−π2
Similarly, sin(2x)=sin(2x−2π)=cos(π2−2x−2π)
So we see that
(π2−2x−2π)=±3x
iii)
π2−2π=5x
x=−310π
iv)
π2−2π=−x
x=2π−π2=32π
Finally, we note that the solutions must repeat every 2π because the original functions each repeat every 2π. (The sine function has period π so it has completed exactly two periods over an interval of length 2π. The cosine has period 23π so it has completed exactly three periods over an interval of length 2π. Hence, both functions repeat every 2π2π2π so every solution will repeat every 2π.)
So we get ∀n∈N
i) x=π10+2πn
ii) x=−π2+2πn
iii) x=−310π+2πn
(Note that solution (iv) is redundant since 32π+2πn=−π2+2π(n+1).)
So we conclude that there are really three solutions and then the periodic extensions of those three solutions.
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Answer: 346.4
Step-by-step explanation:
The whole triangle ABD is a 30-60-90 right triangle. In 30-60-90 triangles, the smallest side is x, the middle side is x
, and the largest side/hypotenuse is 2x.
Side AB is the smallest side and therefore x=300. Side BD is the middle side and so we can use x and we get BD=300=519.615
The question is asking for CD, and we know that CD can be equal to BD minus BC since that would isolate CD
Triangle ABC is also a 30-60-90 triangle but the 300 feet is the middle side in this triangle. So we can do 300=x and divide 300 by radical 3 and get that x=173.205
Side BC is the smallest side of this triangle so it would be x and x is 173.205.
Now that we have the whole side BD and the part of it BC. We can subtract BD by BC (519.615-173.205) and we get that CD=346.4
The thousand place
Of 6.589 is 0.009 because after the decimal it goes tenths hundredth then thousands
