Fundamental relations between the trigonometric ratios of an angle:
To know the relations between the trigonometric ratios from the above figure, we see;
sin θ = perpendicular/hypotenuse = MP/PO and
cosec θ = hypotenuse/perpendicular = PO/MP
It is clear that one
is the reciprocal of the other.
So, sin θ = 1/cosec θ and
cosec θ = 1/sin θ ………. (a)
Again, cos θ = base/hypotenuse = OM/OP and
sec θ = hypotenuse/ base = OP/OM
One is reciprocal of the other.
That is, cos θ = 1/sec θ and sec θ = 1/cos θ ………. (b)
So, tan θ = perpendicular/base = MP/OM and cot θ = base/perpendicular = OM/MP
tan θ = 1/cot θ and cot θ = 1/tan θ ………. (c)
Moreover, sin θ/cos θ = (MP/OP) ÷ (OM/OP) = (MP/OP) × (OP/OM) = MP/OM = tan θ
Therefore, sin θ/cos θ = tan θ ………. (d)
and cos θ/sin θ = (OM/OP) ÷ (MP/OP) = (OM/OP) × (OP/MP) = OM/MP = cot θ
Therefore, cos θ/sin θ = cot θ ………. (e)
Sin θ = PM/OPThis is how the ratios are related to show that one is the reciprocal of the other according to the relations between the trigonometric ratios.
Relations Between the Trigonometric Ratios
Problems on Trigonometric Ratios
Reciprocal Relations of Trigonometric Ratios
Problems on Trigonometric Identities
Elimination of Trigonometric Ratios
Eliminate Theta between the equations
Verify Trigonometric Identities
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