Question 459602: what is the exact value for
sec(-5pi/6)
I know the equation is 1/cos
but is it negative sqrt(3)/2 or positive?
or is it negative 1/2 or positive?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! what is the exact value for
sec(-5pi/6)
I know the equation is 1/cos
but is it negative sqrt(3)/2 or positive?
or is it negative 1/2 or positive?
..
In order to determine whether a trig function is positive or negative, we must determine the quadrant the reference angle is in.
For given function, sec(-5π/6), you correctly stated it is 1/cos(-5π/6)
To find which quadrant the function is in, starting from 0 at the right side of the x-axis, rotate clockwise five π/6's or five 30º angles, which puts the terminal side just 30º short of 180º.
(rotate clockwise for negative angles and counter-clockwise for positive angles)
This makes the reference angle π/6 or 30º which gives cos 30º=√3/2 or a sec value of 2/√3=2√3/3. This also places the reference angle in quadrant III where the cosine is negative.
Thus, sec(-5pi/6)=-2√3/3
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