Question

Match the following trigonometric functions in column I with the correct domain and range in column II and column III respectively and choose the correct option from the codes given below.

Column I	Column II	Column III
1. sine	(A) $R-\{x:x=(2n+1)\frac{\pi }{2},n\in Z\}$	(E) $[-1,1]$
2. Cosine	(B) $R-\{x:x=n\pi ,n\in Z\}$	(F) $R-(-1,1)$
3. Tangent	(C) R	(G)R
4. Cotangent
5. Secant
6. Cosecant

• A. 1 - (C, E), 2 - (C, E), 3 - (A, G), 4 - (B, G), 5 - (A, F), 6 - (B, F)
• B. 1 - (C, E), 2 - (B, E), 3 - (A, G), 4 - (B, G), 5 - (B, F), 6 - (A, F)
• C. 1 - (C, E), 2 - (B, F), 3 - (A, G), 4 - (B, G), 5 - (B, E), 6 - (B, F)
• D. 1 - (B, E), 2 - (A, E), 3 - (A, G), 4 - (B, E), 5 - (B, F), 6 - (A, F)

Answer 1

Answer: (A)

The trigonometric functions are defined as follows
Sine function, i.e., $\sin :R\to [-1,1]$
Cosine function, i.e., $\cos :R\to [-1,1]$
Tangent function, i.e., $\tan :R-\left\{x:x=(2n+1)\frac{\pi }{2},n\in Z\right\}$
$\to R$
Cotangent function, i.e., cot : $R-\{x:x=n\pi ,n\in Z\}\to R$
Secant function, i.e., $\sec :R-\{x:x=(2n+1)\frac{\pi }{2}$, $n\in Z\}\to R-(-1,1)$
Cosecant function, i.e.,cosec : $R-\{x:x=n\pi ,n\in Z\}\to R$ $-(-1,1)$