Find all values of x between 0 and

Aliyah Mendez

Aliyah Mendez

Answered question

2022-04-12

Find all values of x between 0 and 4 for which sin(2x+1)=cos(2x+1)
tan(2x+1)=1
Which I believe is correct.
Now the problem is , the range .
If the range is 0 to 2π I would've known how to do but what about the 0 to 4 ?

Answer & Explanation

enchantsyseq

enchantsyseq

Beginner2022-04-13Added 19 answers

use that
sin(x)cos(x)=2sin(π4x)
analiticozuod

analiticozuod

Beginner2022-04-14Added 10 answers

Let ϕ be the smallest value greater than 0 such that tanϕ=1. Let θ be the smallest value greater than 0 such that tan(ϕ+θ)=1. tan is periodic, and θ is the length of this period, so we only need to find the first value and the number of values of ϕ+nθ that occur within the interval specified by 2x+1 for x(0,4)
The interval transformation is easy, we get (1,9). Then we have to compare ϕ=π4 and θ=π with this interval, and we get a first value of ϕ+θ=54π. What should the total number of values be?
Further hint: you can use that 3<π<4 and 6<2π<7?

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