Let us empathize through the next discussion:
Suppose that betoken A(x, y), length OA = r together with angle AOX = α.
Look at the flick above. From correct triangle inwards quadrant I, apply:
- sin α = y/r
- cos α = x/r
- tan α = y/x
Example:
Let A(-12, 5) together with ∠XOA = α, Find the value of sin α together with tan α!
Answer:
By observing the coordinates of betoken A(-12, 5), it is really clear that the points are located inwards the 2nd quadrant, since x = -12, together with y = 5.
Geometrically, presented inwards the flick below:
Since x = -12, together with y = 5, using the phytagoras theorem obtained yesteryear the oblique side, r = 13. Therefore it is obtained:
- sin α = 5/13
- tan α = -5/12
Properties of Quadrant Location
- If 0 < α < (π / 2), hence the value of sine, cosine, together with tangent are positive.
- If (π / 2) < α < π, hence the sine value is positive together with the cosine together with tangent values are negative.
- If π < α < (3π / 2), hence the tangent value is positive together with the sine together with cosine values are negative.
- If (3π / 2) < α < 2π, hence the cosine value is positive together with the sinus together with tangent value is negative.
Similarly this article.
Sorry if at that topographic point is a incorrect word.
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Referensi :
- Book of math senior high schoolhouse course of educational activity x Semester 2