Question

If sin A 4/5 then find cosec theta

Answer 1

GivEn:

• Sin A = 4/5

To find:

• Cosec A?

Solution:

• Let's consider ABC is a triangle.

Where,

• Opposite = 4
• Hypotenuse = 5

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« Now, By using Pythagoras Theorem,

→ (Hypotenus)² = (Perpendicular)² + (Base)²

→ (5)² = (4)² + (b)²

→ 25 = 16 + (b)²

→ b² = 25 - 16

→ b² = √9

→ b = 3

∴ Hence, Base is 3 units.

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« Let's find Cosec A,

We know that,

Cosec = hyp/per

Here,

• Hyp = 5
• Per = 4

Therefore,

→ CosecA = 5/4

∴ Hence, Cos A = 5/4

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More to know:

Trigonometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trigonometric relations

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trigonometric ratios

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj