Question

Trig Graphs

Answer 1

\[y = -\sec(\frac{ \pi }{ 2}x + \frac{ \pi }{ 2 })\]

How does that become this:

\[y = \csc \frac{ \pi x }{ 2 }\]

Answer 2

csc means cosec right?

Answer 3

Yes

Answer 4

\[-\sec(\frac{ \pi }{ 2 }x+\frac{ \pi }{ 2 })=\frac{ -1 }{ \cos(\frac{ \pi }{ 2 }x+\frac{ \pi }{ 2 }) }\]
\[=\frac{ -1 }{ \cos(\frac{ \pi }{ 2 }x)\cos(\frac{ \pi }{ 2 }) -\sin(\frac{ \pi }{ 2 }x)\sin(\frac{ \pi }{ 2 })}\]
\[=\frac{ -1 }{0 -\sin(\frac{ \pi }{ 2 }x) }\]

Answer 5

\[\frac{ 1 }{ \sin (\frac{ \pi }{ 2}x) }=\csc(\frac{ \pi }{ 2}x)\]

Answer 6

Did you get that??

Answer 7

Refer these for Trigonometric and Geometric Conversions
https://www.math10.com/en/geometry/trigonometry-and-geometry-conversions/trigonometry.html
http://mathinstructor.net/2012/08/values-of-trigonometric-ratios-for-0-30-45-60-and-90-degrees/