Notice in particular the ratios which are positiveĪlso, note that `sin theta` is defined as `y/r`, and `cos theta` is defined as `x/r` and `tan theta` is defined as `y/x`. Here's an interactive graph where you can explore trigonometric ratio concepts.ĭrag the point P around the curve into all 4 quadrants and observe the sin, cos and tan ratios These signs are important when we are finding an angle from These just follow from the sign (+ or -) of x or In the fourth quadrant (IV), cos (and sec) are In the third quadrant (III), tan (and cotan) are In the second quadrant (II), sine (and cosec) are It means: In the first quadrant (I), all ratios We use this diagram to remember what ratios are positive in We don't need to remember the reciprocal ones off by heart, but it is recommended that you remember where `sin theta`, `cos theta` and `tan theta` are positive. In Quadrant IV, `sec theta` is positive, `csc theta` and `cot theta` are negative. Unit Circle Trigonometry Coordinates of Quadrantal Angles and First Quadrant Special Angles First, we will draw a right triangle that is based on a 30o reference angle. In Quadrant III, `cot theta` is positive, `csc theta` and `sec theta` are negative. In Quadrant II, `csc theta` is positive, `sec theta` and `cot theta` are negative. Of course the reciprocal ratios, `csc theta`, `sec theta` and `cot theta` follow the same pattern: In Quadrant IV, `cos theta` is positive, `sin theta` and `tan theta` are negative. In Quadrant III, `tan theta` is positive (both x and y are negative, so `y/x` is positive), `sin theta` and `cos theta` are negative. In Quadrant II, `sin theta` is positive, `cos theta` and `tan theta` are negative. So `cos theta` will always be negative there, too.įor the `tan theta` case, y is positive and x is negative, so `y/x` will always be negative.Ĭonsidering the other quadrants, we see a pattern. 1050 - 360 690 - 360 330 330 lies in quadrant IV 360 - 330 30, so the reference angle is 30. In the second quadrant, x is always negative. So we conclude `sin theta` is always going to be positive in the second quadrant.Īlso observe for (in the `cos theta` case), that x was negative. Since r is always positive, then `y/r` will always be positive in quadrant II. Also notice that in the second quadrant, the y-value is positive. Observe for the example above, that our angle was in the second quadrant. The coordinate plane has four quadrants, and it is important that. 2nd Quadrant: The upper left-hand corner of the graph is the second quadrant. In this quadrant the values of x and y both are positive. 1st Quadrant: The upper right-hand corner of the graph is the first quadrant.
`cot theta=x/y=(-2)/3=-0.6667` The Four Quadrants - Positive or Negative? Students who searched for teaching math quadrants 5th grade found the information and. Well, the graph is divided into sections or four quadrants, based on those values.
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