If \(\cos(2x - 1) = \sin(3x + 6)\), then what is the value of \(x\)?

2x - 1 + 3x + 6 = 90° 5x + 5 = 90 5x = 90 - 5 5x = 85 x = 85/5 x = 17°

Answered by Hypatia | 2024-06-10

The value of** x** in expression cos(2x-1) = sin(3x+6) is** 17.**

cos(2x-1) = sin(3x+6)
let
a = 2x - 1
b = 3x + 6
Therefore,
cos a = sin b
Therefore, a and b are** complimentary**.
What is complimentary angle?
**Complimentary angles **are angles that sum up to 90 degrees. Therefore,
2x - 1 + 3x + 6 = 90
2x + 3x - 1 + 6 = 90
5x + 5 = 90
5x = 90 - 5
5x = 85
x = 85 / 5
x = 17

learn more on** trigonometry** here: https://brainly.com/question/2193114

Answered by vintechnology | 2024-06-16

The value of x that satisfies the equation cos ( 2 x − 1 ) = sin ( 3 x + 6 ) is x = 17 . By utilizing the identity cos ( a ) = sin ( 9 0 ∘ − a ) , we successfully transformed and solved the equation. This step-by-step process leads us to our solution clearly.
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Answered by vintechnology | 2024-10-01