Q. 44.0( 13 Votes )

In the figure 8.15 PQR = 900, PQS = 900, PRQ = α and QPS = θ Write the following trigonometric ratios.

i. sin α, cos α, tan α

ii. sin θ, cos θ, tan θ


Answer :

For any right-angled triangle,

sinθ = Opposite side Side/Hypotenuse


cosθ = Adjacent sideSide/Hypotenuse


tanθ = sinθ/cosθ


= Opposite side Side/Adjacent sideSide


cotθ = 1/tanθ


= Adjacent sideSide/Opposite side Side


secθ = 1/cosθ


= Hypotenuse/Adjacent sideSide


cosecθ = 1/sinθ


= Hypotenuse/Opposite side Side


(i) In the given triangle let us understand, the Opposite side and Adjacent sidesides.


So, for Δ PQR,


So, for α,


Opposite side Side = PQ


Adjacent sideSide = QR


In general for the side Opposite side to the 90° angle is the hypotenuse.


So, for Δ PQR, hypotenuse = PR


sin α = Opposite side Side/Hypotenuse


= PQ/PR


cos α = Adjacent sideSide/Hypotenuse


= QR/PR


tan α = sinθ/cosθ


= Opposite side Side/Adjacent sideSide


= PQ/QR


(ii) In the given triangle let us understand, the Opposite side and Adjacent sidesides.


So for Δ PQS,


So for θ,


Opposite side Side = QS


Adjacent sideSide = PQ


In general for the side Opposite side to the 90° angle is the hypotenuse.


So for Δ PQS, hypotenuse = PS


sinθ = Opposite side Side/Hypotenuse


= QS/PS


cosθ = Adjacent sideSide/Hypotenuse


= PQ/PS


tanθ = sinθ/cosθ


= Opposite side Side/Adjacent sideSide


= QS/PQ


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