If x ∈ [ 0 , 4 π ] and y ∈ [ 0 , 4 π ] , then the number of ordered pairs ( x , y ) that satisfy the equation sin − 1 ( sin x ) + cos − 1 ( cos y ) = 2 3 π are:

Question

If x ∈ [ 0 , 4 π ] and y ∈ [ 0 , 4 π ] , then the number of ordered pairs ( x , y ) that satisfy the equation sin − 1 ( sin x ) + cos − 1 ( cos y ) = 2 3 π ​ are:

TestHub · Accepted Answer

sin − 1 sin x ≤ 2 π ​ , cos − 1 cos y ≤ π hence sin x = 1 , cos y = − 1 Ordered pairs ( 2 π ​ , π ) , ( 2 π ​ , 3 π ) , ( 2 5 π ​ , π ) , ( 2 5 π ​ , 3 π ) are the solution.

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

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