Mathematics Dictionary Dr. K. G. Shih

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Unit Circle and Unit Hyperbola

Subjects

Read Symbol defintion Q01 | - Unit circle Q02 | - Unit Hyperbola Q03 | - Compare diagram of x=tan(t) and y=sec(t) with diagram of x=sec(t) and y=tan(t) Q04 | - Q05 | - Q06 | - Q07 | - Q08 | - Q09 | - Q10 | -

Answers

Q01. Unit circle Parametric equations : x = cos(t) and y = sin(t) is unit circle. Proof x^2 + y^2 = cos(t)^2 + sin(t)^2. Since cos(t)^2 + sin(t)^2 = 1. Hence x^2 + y^2 = 1. This is a circle with center at (0,0) and radius = 1. Study subject Find diagram of x = cos(t) and y = sin(t). Go to Begin Q02. Unit hyperbola Parametric equations : x = tan(t) and y = sec(t) is unit hyperbola. Proof Since tan(t)^2 + 1 = sec(t)^2. Hence x^2 + 1 = y^2. Hence x^2 - y^2 = -1. This is a hyperbola with center at (0,0) and semi-axese = 1. Study subject Find diagram of x = tan(t) and y = sec(t). Go to Begin Q03. Compare diagram of x=tan(t) and y=sec(t) with diagram of x=sec(t) and y=tan(t) x = tan(t) and y = sec(t) give x^2 - y^2 = -1. Principal axis x = 0. x = sec(t) and y = tan(t) give x^2 - y^2 = +1. Principal axis y = 0. Study subject See diagram for comparison. Go to Begin Q04. Answer Go to Begin Q05. Answer Go to Begin Q06. Answer Go to Begin Q07. Answer Go to Begin Q08. Answer Go to Begin Q09. Answer Go to Begin Q10. Answer Go to Begin

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