Which function matches the graph? a. y=3csc(1/2x) b. y=1/3sec(2x) c. y=sec(1/2x)+3 d. y=3sec(1/2x)

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Which function matches the graph? a. y=3csc(1/2x) b. y=1/3sec(2x) c. y=sec(1/2x)+3 d. y=3sec(1/2x)

Mathematics
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probably best to know what csc, sec, reduce to in sin, cos, tan etc...
the amplitude is 3, I know that, and I think it is a secant graph. So I am guessing the answer is d. am I right?

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Other answers:

\[\csc(x)=\frac{ 1 }{ \sin(x) }; {\space}\sec(x)=\frac{ 1 }{ \cos(x) }\]
so we can reduce our equations to either: \[y=\frac{ 3 }{ \sin(\frac{ x }{ 2 })}\] \[y=\frac{ 1 }{ 3\cos(2x) }\] \[y=\frac{ 1 }{ \cos(\frac{ x }{ 2 }) }+3\] \[y=\frac{ 3 }{ \cos(\frac{ x }{ 2 }) }\]
okay that sorta makes sense but i am a visual learner so
btw, when you write sec(1/2x) is that \[\sec(\frac{ x }{ 2 })\] or \[\sec(\frac{ 1 }{ 2x })\]
yes d looks right
cool thanks

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