Cambridge Additional Mathematics

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