math_knight
New member
- Joined
- Jun 13, 2018
- Messages
- 13
The book points out how cos(t) and sec(t) are even functions (how f(-x)= f(x)), and then it shows the graph of two angles in Quadrant I and IV. t= 1/6 pi and t = - 1/6 pi.
The book sorta glosses over the topic and then goes on to give examples of angles that are conveniently on Quadrant I or IV, where x is positive.
But what about an angle of -2/3 pi, both x, and y are negative. A negative/negative = positive but what about angel t = 2/3 pi?
a.) one way which the book taught was just to think of cos (t) as the x- coordinate (if using a unit circle), in which case x would be negative for t=-2/3 pi and 2/3 pi
AND
b.) my ti-92 says cos(-2/3 pi) = -.5 --> cos(-x) = -cos (x) --> f(-x) = -f(x) --> odd function
AND
c.) my ti-92 says cos (2/3 pi) = -.5 also
d.) The "All Student Take Calculus mnemonic" says cos (t) would only be positive in the I and IV Quadrant...cos(2/3 pi) is in Quadrant II
A bit confusing when you introduce odd/even concept. I must not have a clear conceptualization of f(-x) = f(x)?
EVEN function means ---> function(negative input)=output still positive?
I hope I didn't belabor the topic...any help would be appreciated.
The book sorta glosses over the topic and then goes on to give examples of angles that are conveniently on Quadrant I or IV, where x is positive.
But what about an angle of -2/3 pi, both x, and y are negative. A negative/negative = positive but what about angel t = 2/3 pi?
a.) one way which the book taught was just to think of cos (t) as the x- coordinate (if using a unit circle), in which case x would be negative for t=-2/3 pi and 2/3 pi
AND
b.) my ti-92 says cos(-2/3 pi) = -.5 --> cos(-x) = -cos (x) --> f(-x) = -f(x) --> odd function
AND
c.) my ti-92 says cos (2/3 pi) = -.5 also
d.) The "All Student Take Calculus mnemonic" says cos (t) would only be positive in the I and IV Quadrant...cos(2/3 pi) is in Quadrant II
A bit confusing when you introduce odd/even concept. I must not have a clear conceptualization of f(-x) = f(x)?
EVEN function means ---> function(negative input)=output still positive?
I hope I didn't belabor the topic...any help would be appreciated.