untitled

From the figure :

sinθ=

OP

PM

= [sine of angle θ]

cosθ=

OP

OM

= [cosineof angle θ]

tanθ=

OM

PM

= [tangentof angleθ]

And opposite ratios of them are

cosecT =
sinθ

1

[cosecant of angle θ]

secθ =

cosθ

1

[secantof angle θ]

cotθ =

tanθ

1

[cotangent of angle θ]

We observe, the symbol sinθ means the ratio of sine of the angle θ, not the
multiplication of sin and θ.sinis meaningless without θ. It is applicable for the other
trigonometric ratios as well.

9 ⋅ 4 Relation among the trigonometric ratios

Let, ‘XOA θ is an acute angle.
from the adjacent figure, according to the definition

sinθ=

OP

PM

, cosecT =

sinθ

1

=

PM

OP

cosθ=

OP

OM

, secθ=

cosθ

1

=

OM

OP

tanθ=

OM

PM

, cotθ =

tanθ

1

=

PM

OM

Again, tanθ =
OM

PM

OP

OM

OP

PM

[Dividing the numerator and the denominator by OP]

=
θ

θ

cos

sin

? tanθ =

θ

θ

cos

sin

and similarly

cotθ =

θ

θ

sin

cos

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