Question

if cos theta= 3/2 then find the value of cosec theta​

Answer 1

$\bf\underline{\underline{\green{SOLUTION:-}}}$

Question

• If cos theta= 3/2 then find the value of cosec theta?

Answer

• Value of Cosec θ = 2/√-5

Given

• Cosθ = 3/2

To Calculate

• Value of Cosec θ ?

Explanation

Cosθ = 3/2 ( Given)

Cos θ = Base / Hypotenuse

Base = 3

Hypotenuse = 2

By Pythagoras theorem

h² = p²+b²

2²=p²+3²

4=p²+9

4-9= p²

p² = -5

p= √-5

Cosec θ = hypotenuse/perpendicular

Cosec θ = 2/√-5

$\bf\underline{\underline{\green{HENCE:-}}}$

• Value of Cosec θ = 2/√-5

_________________________________________

Answer 2

$\Large{\underline{\underline{\mathfrak{\red{\bf{Solution}}}}}}$

$\Large{\underline{\mathfrak{\orange{\bf{Given}}}}}$

• Cos θ = 3/2

$\Large{\underline{\mathfrak{\orange{\bf{Find}}}}}$

• Value of Cosec θ.

$\Large{\underline{\underline{\mathfrak{\red{\bf{Explanation}}}}}}$

Important Formula

$\star{\tt{\green{\:\cos \theta\:=\:\dfrac{Base}{Hypotenuse}}}}$

$\star{\tt{\green{\:\cosec \theta\:=\:\dfrac{Hypotenuse}{Perpendicular}}}}$

Pythagoras Theorem,

$\boxed{\tt{\blue{\:(Hypotenuse)^2\:=\:(Base)^2+(Perpendicular)^2}}}$

Let, Here PQR is a right triangle.

Where,

• AB = Perpendicular
• BC = Base
• CA = Hypotenuse

Given Here,

➡ Cos θ = 3/2 = Base/Hypotenuse = BC/CA

Now, using Pythagoras Theorem,

➡ (Hypotenuse)² - (Base)² = (Perpendicular)²

Keep all above values

➡ (Perpendicular)² = 2² - 3²

➡ (Perpendicular)² = 4 - 9

➡(Perpendicular)² = -5

➡(Perpendicular) = √(-5)

Since, Now

➡ Cosec θ = (Hypotenuse)/(Perpendicular)

Keep values,

➡ Cosec θ = 2/(√-5)

$\Large{\underline{\underline{\mathfrak{\red{\bf{Hence}}}}}}$

• Value of Cosec θ will be = 2/(√-5)

__________________