Question

The value of sin1 cos 2 tan 3 cot 4 sec 5 cosec 6 is
A.positive
B.negative
C.zero
D.may be positive and negative

Answer 1

Hint: We will have to find the quadrant for each trigonometric function given, then according the signs will be given to them and lastly multiply all the sign (+ ve or – ve) to get the resultant sign

Complete step-by-step answer:
We know that each quadrant in the graph holds + ve and – ve values for different trigonometric signs.
Like sin function is + ve in 1st quadrant and 2nd cos functions is + ve in 1st quadrant and 4th quadrant tan function is + ve in 1st and 3rd quadrant.

and similarly for their reciprocal functions. i.e., Cos ⟶ Sec, Sin ⟶ Cosec, tan ⟶ cot.

So here we will make a chart to know about the quadrant of the angle and it is + ve or – ve

     Quadrant Sign
Sin 1 ⟶ Sin (1 st quadrant +) = + ve
Cos 2 ⟶ Cos (2nd quadrant +) = – ve
Tan 3 ⟶ tan (2rd quadrant +) = – ve
Cot 4 ⟶ Cot (3rd quadrant + ) = + ve
Sec 5 ⟶ Sec (4th quadrant +) = + ve
Cosec 6 ⟶ Cosec (4th quadrant) = - ve
So here 3 are + ve and 3 are – ve as we know + ve × + ve = + ve and – ve × + ve = – ve
So, from above,
=+ ve × + ve × + ve × – ve × – ve × – ve
= – ve.
So, therefore the value of Sin 2 cos 2 tan 3 cot4 sec 5 cosec 6 is – ve
Hence, B is the correct option.


Note: In this type of question, we need to know about quadrant system and which function is + ve in which quadrant and secondly, we need to figure out the quadrants by looking into the angles for e.g. here Sin 1 it lies in 1st quadrant.