# Find sin, cos, and tan for a given quadrant angle

Find (a) sin ∅, (b) cos ∅, and (c) tan ∅ for the given quadrantal angle. If the value is undefined, write “undefined.” My quadrantal angle is -450°

Sin = opp/hyp

I drew a graph and put the angle -450° in the 3rd quadrant because both x and y are negative and I assumed since my degree is in negative it would have to be in there. I am stuck on how to actually solve the problem. My teacher gave us the answers but we have to show our work, it is just very confusing because he isn't good at explaining at all so I am lost.

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Doc Al
Mentor
I drew a graph and put the angle -450° in the 3rd quadrant
Where exactly is the angle? What angle below the x-axis, for instance?

Where exactly is the angle? What angle below the x-axis, for instance?

it does not say. that is what confuses me. i just took a random guess that it was in the 3rd quadrant

Doc Al
Mentor
it does not say. that is what confuses me. i just took a random guess that it was in the 3rd quadrant
Why guess? You have the angle, so mark exactly where it must appear. What if the angle were -30°? -90°?

HallsofIvy
Homework Helper
Find (a) sin ∅, (b) cos ∅, and (c) tan ∅ for the given quadrantal angle. If the value is undefined, write “undefined.” My quadrantal angle is -450°

Sin = opp/hyp

I drew a graph and put the angle -450° in the 3rd quadrant because both x and y are negative
Here is your first error. How do you know "both x and y are negative"? You are not told what x and y are!

and I assumed since my degree is in negative it would have to be in there.
Now you are contradicting yourself. Before you said the angle is in the third quadrant because x and y are negative, now you are saying the angle is in the third quadrant ("x and y are negative") because the angle is negative.

Surely you know better than that! A "positive" angle is measured counter clockwise and sweep all the way around the circle, through all quadrants- possibly many times. A "negative" is measured clockwise but still sweeps through all quadrants.

The crucial point here is that a full circle is 360 degrees- and then we start the circle anew (the trig functions have period 360 degrees). -450 is less than -360 degrees. That's why jayanthd added 360 degrees: "backing up" a full circle leaves us at the same point on the circle as -450+ 360= -90 degrees. Where is that on the unit circle?

I am stuck on how to actually solve the problem. My teacher gave us the answers but we have to show our work, it is just very confusing because he isn't good at explaining at all so I am lost.
Your teacher isn't very good at explaining or you aren't very good at understanding? If it is the latter then you are capable of improving. Which would you rather think?