The most general value of x satisfying the equations tan &#x2061;<!-- ⁡ --> x = &#x2

Ayanna Trujillo

Ayanna Trujillo

Answered question

2022-06-15

The most general value of x satisfying the equations tan x = 1 and cos x = 1 / 2 , is found to be x = 2 n π + 7 π 4

Answer & Explanation

Blaine Foster

Blaine Foster

Beginner2022-06-16Added 33 answers

tan θ = 1 = tan ( 3 π 4 ) = tan ( 7 π 4 )
tan ( π 3 π 4 ) = tan ( π + 3 π 4 )
cos θ = 1 2
cos π 4 = 1 2
cos ( 2 π 7 π 4 ) = 1 2 = cos 7 π 4
Hence, the principal value for both tan θ and cos θ is 7 π 4
Thus, the general value of θ is 2 n π + 7 π 4

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