Posted by Crystal on Saturday, November 24, 2012 at 8:07pm.
Though they aren't homework questions I really am desperate to understand the answers to these questions as I have a quiz tomorrow
Always sketch the problem on your x-y coordinate system. Look at what is positive and what is negative in each quadrant.
But why is the sin, cos, and tan of the principal angle equal to the sin, cos, and tan of the related acute angle?
Huh? I am not sure what you mean or why you said that.
For example draw your angle 110 degrees
That is in quadrant 2 20 degrees left of straight up
now the tangent is -2.75 as we know. x is - and y is +
Now draw that angle of 290 degrees in quadrant 4 which is 20 degrees to the right of straight down. In fact it is the extension of the first line . x is + and y is -
the tangent is again -2.75
HOWEVER
the sin of 110 is +.94 because y is +
the sin of 290 is -.94 because y is -
If you want the angle with the same sin as 110, you must go where y is +
That is in quadrant 1
sin 70 = + .94
in quadrant 1
sin is +
cos is +
tan is +
in quadrant 2
sin is +
cos is -
tan is -
in quadrant 3
sin is -
cos is -
tan is +
in quadrant 4
sin is -
cos is +
tan is -
The related acute the angle between the ray and the x or y axis. however the sign depends on the quadrant.
I asked that because that's what it says in my notes, and I don't understand it;
But thank you for all the help you've given me
the thing is that 70 degrees, 110 degrees, 250 degrees and 290 degrees are all 20 degrees from the vertical axis and have the same absolute values of trig functions
HOWEVER the signs depend on the quadrant
Thanks! That makes total sense; I understand how to get the equivalent expressions now (:
And I'll definitely remember the signs