P
Q,(1tan_μ)
A,(1 0)
x
y
μ
O
P
Q,(1tan¡μ)
A,(1 0) x
y
μ
O
-^32 ¼ -¼ -¼ 2 ¼ 2 ¼^32 ¼ 2 ¼^52 ¼
P
Q,(1¡¡tanμ)
A,(1 0)¡
x
y
μ
O
x
y
A,() 10 ¡
tan¡μ
Q,(1¡¡tanμ)
P
μ
cos¡μ
N
1
1
-1
-1 tangent
O
sin¡μ
238 Trigonometric functions (Chapter 9)
We have seen that if P(cosμ,sinμ) is a point which is free
to move around the unit circle, and if [OP] is extended to meet
the tangent at A(1,0), the intersection between these lines
occurs at Q(1,tanμ).
This enables us to define thetangent function
tanμ=
sinμ
cosμ
Forμin quadrant 2 , sinμ is positive and cosμ is negative
and so tanμ=
sinμ
cosμ
is negative.
As before, [OP] is extended to meet the tangent at A at
Q(1,tanμ). We see that Q is below thex-axis.
Forμin quadrant 3 , sinμ and cosμ are both negative and
so tanμ is positive. This is clearly demonstrated as Q is back
above thex-axis.
Forμin quadrant 4 , sinμ is negative and cosμ is positive.
tanμ is again negative. We see that Q is below thex-axis.
Discussion
#endboxedheading
What happens totanμwhen P is at(0,1)and(0,¡1)?
D The tangent function
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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_09\238CamAdd_09.cdr Monday, 6 January 2014 4:42:08 PM BRIAN