Find the exact values of the six trigonometric ratios of the angle θ in the triangle?

Solution:

From the figure,

Opposite = 200

Hypotenuse = 205

By pythagoras theorem,

a² + b² = c²

So, (200)² + b² = (205)²

⇒ 40000 + b² = 42025

⇒ b² = 42025 - 40000

⇒ b² = 2025

Taking square root,

⇒ b = 45

So, adjacent = 45

We have to find the exact values of the six trigonometric ratios of the angle θ in the triangle.

⇒ We know, sin θ = opposite/hypotenuse

sin θ = 200/205

sin θ = 0.9756

⇒ cos θ = adjacent/hypotenuse

cos θ = 45/205

cos θ = 0.2195

⇒ tan θ = opposite/adjacent

tan θ = 200/45

tan θ = 4.4444

⇒ cosec θ = hypotenuse/opposite

cosec θ = 205/200

cosec θ = 1.025

⇒ sec θ = hypotenuse/adjacent

sec θ = 205/45

sec θ = 4.5556

⇒ cot θ = adjacent/opposite

cot θ = 45/200

cot θ = 0.2250

Therefore, the exact values of six trigonometric ratios are sin θ = 0.9756, cos θ = 0.2195, tan θ = 4.4444, 

cosec θ = 1.025, sec θ = 4.5556 and cot θ = 0.2250.

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Find the exact values of the six trigonometric ratios of the angle θ in the triangle?

Summary:

The exact values of the six trigonometric ratios of the angle θ in the triangle are sin θ = 0.9756, cos θ = 0.2195, tan θ = 4.4444, cosec θ = 1.025, sec θ = 4.5556 and cot θ = 0.2250.