Question

Tell me the ranges of sinA,cosA,tanA,cotA,secA,cosecA.​

Answer 1

Solution:-

* Sine Function

$\implies\rm \: f(A) = \sin A$

$\rm \to \: domain \: \in \: R$

$\rm \: \to \: range \in[ - 1,1 ]$

* Cosine function

$\rm \implies \: f(A) = \cos A$

$\rm \to \: domain \: \in \: R$

$\rm \to \: \: range \in[ - 1,1 ]$

* Tangent function

$\rm \implies \: f(A) = \tan A$

$\rm \to \: domain \in \: R \: - \bigg \{ \dfrac{(2n + 1) \pi}{2} ,n \in \: z \bigg \}$

$\rm \to \: range \: \in \: R$

* Cosecant function

$\implies\rm \: f(A) = \csc \: A$

$\rm \to \: domain \: \in \: R \: - \{n\pi,n \in \: z \}$

$\to \: \rm \: range \in \: R \: - ( - 1,1)$

* Secant function

$\rm \implies \: f(A) = \sec \: A$

$\rm \to \: domain \in \: R - \{(2n + 1) \dfrac{\pi}{2} ,n \in \: z \}$

$\rm \to \: range \: \in \: R - ( - 1,1)$

* Cotangent function

$\rm \implies \: f(A) = \cot A$

$\rm \to \: domain \in \: R - \{n\pi,n \in \: z \}$

$\rm \: \to range \in \: R$