Show that f is continuous on (-infty , infty). f(x)={(sin(x) if x<pi/4),(cos(x) if xge pi/4):}

Nelson Jennings 2022-07-25 Answered
Show that f is continuous on ( , ).
f ( x ) = { sin ( x )   i f   x < π / 4 cos ( x )   i f   x π / 4
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Answers (1)

Coleman Ali
Answered 2022-07-26 Author has 13 answers
you know that the sine ans cosine functions are continuousbecause all the regions of the graph are defined...the only problemis the transition between the two function at π / 4
so you would have to prove that sin ( π / 4 ) = cos ( π / 4 )
since sin ( π / 4 ) = cos ( π / 4 ) = 2 / 2 = 0.7071
where one functions ends, the other begins, making thetransition seamless and thus, it is a continuous functions.
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