Step-by-step explanation:
Explanation:
The trick is to know about the basic idea of sequences and series and also knowing how i cycles.
The powers of i will result in either: i, −1, −i, or 1.
We can regroup i+i2+i3+⋯+i258+i259 into these categories.
We know that i=i5=i9 and so on. The same goes for the other powers of i.
So:
i+i2+i3+⋯+i258+i259
=(i+i5+⋯+i257)+(i2+i6+⋯+i258)+(i3+i7+⋯+i259)+(i4+i8+⋯+i256)
We know that within each of these groups, every term is the same, so we are just counting how much of these are repeating.
=65(i)+65(i2)+65(i3)+64(i4)
From here on out, it's pretty simple. You just evaluate the expression:
=65(i)+65(−1)+65(−i)+64(1)
=65i−65−65i+64
=−65+64
=−1
So,
i+i2+i3+⋯+i258+i259=-1
Answer:
To solve for the trigonometric functions of x, we need to recall the ratios they represent as shown below.
sin x = O/H
cos x = A/H
tan x = O/A
where O stands for opposite, A for adjacent, and H for hypotenuse. So, for example, the sine of x is equal to the side opposite of angle x over the hypotenuse. The same goes for cosine and tangent. Using the diagram attached, we have the expressions of the trigonometric functions as shown below.
sin x = f/d
cos x = e/d
tan x = f/e
Step-by-step explanation:
Answer: 6
Step-by-step explanation:
They are similar triangles so they have proportionality
For the small triangle the side is 2 and the hypoteneuse is 4, for the large triangle the side is 5 so the entire hypoteneuse is 10. 10-4 = 6 which is the missing side
1x68
2x34
4x17
Hope that helps
