(a) As described in the picture sine and cosine has a period of 2pi because it takes 360 degrees (2pi) for the period to repeat again. In the other hand it only takes tangent and cotangent 180 degrees (pi) for the period to repeat.
(b) In the second picture on the right cosine and sine only have amplitudes of one because it has no asymptotes and in the unit circle they both can equal 1 depending which radians. Tangent can only equal 0 or be undefined. As for csc and sec they are the reciprocals of sin and cosine and when it divided by 0 then it is undefined.
http://faculty.trevecca.edu/sstueckle/courses/Calculus/Practice_Sets/review_trig.htm
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