Question

If sin(θ -π/2) = 0.73.. find cos (-θ) plz explain how to solve

Answer 1

`cos(-\theta) = -0.73`

Explanation:

It is given that:

`sin(\theta -(\pi)/(2)) = 0.73`

Formula to be used:

`1.\ sin(-x) = -sinx\\2.\ sin((\pi)/(2)-x) = cosx\\3.\ cos(-x) = cosx`

Using Formula (1) written above:

`\Rightarrow sin (\theta - (\pi)/(2))=sin(-((\pi)/(2)-\theta ))\\\Rightarrow -sin((\pi)/(2)-\theta)`

Now, using Formula (2) written above:

`\Rightarrow -sin((\pi)/(2)-\theta) = -cos \theta`

So, we can say that:

`sin(\theta -(\pi)/(2)) = -cos\theta = 0.73 ...... (1)`

We have to find the value of
`cos(-\theta)`.

Using Formula (3) written above:

`cos(-\theta) = cos\theta`

So, ultimately we need to find the value of
`cos\theta`

Using equation (1):

`-cos\theta = 0.73\\\Rightarrow cos\theta = -0.73`

So, the answer is
`cos(-\theta) = -0.73`.