# 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 αii. sin θ, cos θ, tan θ For any right-angled triangle,

sinθ = Opposite side Side/Hypotenuse

tanθ = sinθ/cosθ

cotθ = 1/tanθ

secθ = 1/cosθ

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

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

= QR/PR

tan α = sinθ/cosθ

= 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

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

= PQ/PS

tanθ = sinθ/cosθ

= QS/PQ

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