Finding reference angles

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mathmarauder

Junior Member
Joined
Oct 25, 2008
Messages
68
How do you know which way to go when looking for a reference angle?

tan 3pi/4...now i know this equals 135 degrees..to do i go to the 90 degree point or the 180 degree point
most importantly what decides which line to get the reference angle from?
my thoughts on the solutions.
3pi/4 equals 135 degrees - 180 degrees....which gives you -45 degrees.
now that I have 45 degrees im looking for the function value for the reference angle is
cos pi/4 = 1 my question is how does this equal 1.
i probably am making no sense, please help
 
mathmarauder said:
How do you know which way to go when looking for a reference angle?

tan 3pi/4...now i know this equals 135 degrees..to do i go to the 90 degree point or the 180 degree point
most importantly what decides which line to get the reference angle from?
my thoughts on the solutions.
3pi/4 equals 135 degrees - 180 degrees....which gives you -45 degrees.
now that I have 45 degrees im looking for the function value for the reference angle is
cos pi/4 = 1 my question is how does this equal 1.
i probably am making no sense, please help
Click to expand...

The "reference angle" is the acute angle between the terminal side of the given angle and the x-axis.

If your angle is in quadrant II, then the reference angle (in radians) is (pi - angle measure) So, if the angle is 3pi/4, a second quadrant angle, then the reference angle is pi - (3pi/4), or pi/4.

In quadrant III, the reference angle is (angle measure - pi)

In quadrant IV, the reference angle is (2pi - angle measure)

Now...for your specific problem, you were asked to find tan 3pi/4
That's a second-quadrant angle, so the reference angle is pi - (3pi/4), or pi/4

In quadrant II, tan theta is negative. So, tan (3pi/4) = - tan (pi/4)

tan pi/4 = 1
tan (3pi/4) = -1

Where you're getting cos theta from, I don't know!
 
I didnt meant to type the cos theta

Is there a list or table somewhere that says when tan or cos or sin...
is negative?
For example, you are saying in quad ll tan theta is negative.
is there a table or a simple formula that shows me each quad and what
each function woud be whether positive or negative?
 
mathmarauder said:
I didnt meant to type the cos theta

Is there a list or table somewhere that says when tan or cos or sin...
is negative?
For example, you are saying in quad ll tan theta is negative.
is there a table or a simple formula that shows me each quad and what
each function woud be whether positive or negative?
Click to expand...

If you know (and you SHOULD) the definitions for the trig functions based on the coordinates (x, y) of a point on the terminal side of the angle in standard position, then this should be a snap. For example, tan theta = y/x where (x, y) is a point on the terminal side of theta. Suppose theta terminates in quadrant II. For any point in quadrant II, x is negative and y is positive, so y/x must be negative.

This website introduces two little "catch phrases" that may help you remember which functions are positive and which are negative in the various quadrants:

http://planetmath.org/encyclopedia/Dete ... tions.html
 
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