Today in class we learned how to find the six trigonometric functions for any angle.
Defenitions of Trigonometric Functions of Any Angle
Let θ be an angle in standard position with (x,y) a point on the terminal side of θand r = √x^2+y^2 = 0.
sinθ = y/r cosθ = x/r
tanθ = y/x cotθ= x/y
secθ = r/x cscθ = r/y
To evluate these trigonometric functions, when given a point on the terminal side of θ, plug in the coordinates of that point to find r. Then plug in r and the afforementioned cordinates for the above defenitions and have fun.
We also discussed in class the signs of the trigonometric functions in each quadrant.
Quadrant I Quadrant II Quadrant III Quadrant IV
sinθ: + sinθ: + sinθ: - sinθ: -
cosθ: + cosθ: - cosθ: - cosθ: +
tanθ: + tanθ: - tanθ: + tanθ: -
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