Question

in a right angled triangle sin0=5/13. find all the trigonometric ratios for the triangle.​

Answer 1

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Answer 2

Given:

In a right angled triangle sin0=5/13.

To find:

Find all the trigonometric ratios for the triangle.​

Solution:

From given, we have,

In a right angled triangle,

sin ∅ = 5/13.

cosec ∅ = 1/sin ∅

cosec ∅ = 1 / (5/13)

cosec ∅ = 13/5

we know the formula,

sin² ∅ + cos² ∅ = 1

cos² ∅ = 1 - sin² ∅

cos² ∅ = 1 - (5/13)²

cos ∅ = 12/13

tan ∅ = sin ∅/cos ∅

tan ∅ = (5/13) / (12/13)

tan ∅ = 5/12

cot ∅ = 1/tan ∅

cot ∅ = 1 / (5/12)

cot ∅ = 12/5

sec ∅ = 1/cos ∅

sec ∅ = 1 / (12/13)

sec ∅ = 13/12

Therefore, the trigonometric ratios are:

sin ∅ = 5/13, cos ∅ = 12/13, tan ∅ = 5/12, cot ∅ = 12/5, sec ∅ = 13/12, cosec ∅ = 13/5