Solving a trigonometric function How do you solve this trigonometric equation? Solve the equation for solutions in the interval [0,2 pi). (cot(x) -1)( 2 sin(x) + sqrt(3)) = 0.

Gerardo Aguilar

Gerardo Aguilar

Answered question

2022-10-23

Solving a trigonometric function
How do you solve this trigonometric equation?
Solve the equation for solutions in the interval [ 0 , 2 π )
( cot ( x ) 1 ) ( 2 sin ( x ) + 3 ) = 0.

Answer & Explanation

Martha Dickson

Martha Dickson

Beginner2022-10-24Added 20 answers

A product of two real valued quantities is zero if and only if one of the terms in the product is zero.
So, here, either
cot x 1 = 0
or
2 sin x + 3 = 0.
Equivalently either cot x = 1 or sin x = 3 / 2. Can you find the solutions to these? Remember to only take solutions in [ 0 , 2 π ).

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