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natta225 [31]
3 years ago
15

What is the next number in the sequence?

Mathematics
1 answer:
charle [14.2K]3 years ago
8 0
Looks like the next term in the sequence is generated by multiplying the previous term by 3 and adding 1:

1\times3+1=4
4\times3+1=13
13\times3+1=40
40\times3+1=121

If the pattern holds, the next term is probably going to be

121\times3+1=364
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π/4, 5π/4

If cos(x) and sin(x) are defined to you as nonnegative functions (in terms of lengths), then 3π/4 and 7π/4 are also included

Step-by-step explanation:

Remember that odd multiples of 45° are special angles, with the same sine and cosine values (you can prove this, for example, by considering a right triangle with an angle of 45° and hypotenuse with length 1, and finding the trigonometric ratios).

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If you define sin(x) and cos(x) using the cartesian coordinate system (via unit circle), then cos(3π/4)=-sin(3π/4) and cos(7π/4)=-sin(7π/4). In this case, only π/4 and 5π/4 are valid choices.  

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