Question

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

Answer 1

Answer:

$cos(-\theta) = -0.73$

Step-by-step explanation:

It is given that:

$sin(\theta -\dfrac{\pi}{2}) = 0.73$

Formula to be used:

$1.\ sin(-x) = -sinx\\2.\ sin(\dfrac{\pi}{2}-x) = cosx\\3.\ cos(-x) = cosx$

Using Formula (1) written above:

$\Rightarrow sin (\theta - \dfrac{\pi}{2})=sin(-(\dfrac{\pi}{2}-\theta ))\\\Rightarrow -sin(\dfrac{\pi}{2}-\theta)$

Now, using Formula (2) written above:

$\Rightarrow -sin(\dfrac{\pi}{2}-\theta) = -cos \theta$

So, we can say that:

$sin(\theta -\dfrac{\pi}{2}) = -cos\theta = 0.73 ...... (1)$

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 $cos(-\theta) = -0.73$.