Question

Find the General value of theta,when cos (-theta/2) =0​

Answer 1

cos(-theta/2)=cos theta/2

cos 90=0

so,cos theta/2=cos 90

=theta/2=90,theta=180.

theta=180degree

Answer 2

The general solution of 'θ' for the equation cos (-θ/2) = 0 is given by:

θ = (2m ± 1)π where m∈Integers.

Given:

Equation: cos (-θ/2) = 0

To Find:

The general solution for the value of 'θ' in the equation: cos (-θ/2) = 0

Solution:

                                          cos (-θ/2) = 0

∵ cos is an even function:

∴ cos (-θ/2) =  cos (θ/2)

                                       ∴ cos(θ/2) = 0

→ As we know that cos(π/2) = 0

                                       ∴ cos(θ/2) = cos(π/2)

→ For a general equation cosΦ = cosα, the general solution for 'Φ' is given by:

                        Φ = 2nπ ± α where n∈Integers and α∈(o,π]              

∴ For the equation cos(θ/2) = cos(π/2), the general solution is given by:

                               → (θ/2) = 2nπ ± (π/2) where n∈Integers

                                   → θ = 4nπ ± (π) where n∈Integers

                                   → θ = 2mπ ± (π) where m∈Integers

                                  ∴ θ = (2m ± 1)π where m∈Integers

Hence the general solution of 'θ' for the equation cos (-θ/2) = 0 is given by:

                                  θ = (2m ± 1)π where m∈Integers

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