Question

In the given question, $\sin 0^\circ \times \sin 1^\circ .............sin90^\circ = $

A. $0$
B. $\tan 0^\circ $
C. $\sec 90^\circ $
D. $\cos 90^\circ $

Answer 1

Hint – We will note down the question and then we will draw a Trigonometric Ratios Table to find some values. Then we will put the values in the given question and after multiplying them we will get our required answer.

Complete step-by-step answer:

Given, question is,
$\sin 0^\circ \times \sin 1^\circ \times ............. \times \sin 90^\circ $………… (1)

Now, using a trick we will make a Trigonometric Ratios Table, with the help of which we will find the values of the ratios given in the Question.

Look at your left hand, suppose the fingers denote the angles. The thumb denotes $0^\circ $, the index finger denotes $30^\circ $, the middle finger denotes $45^\circ $, the ring finger denotes $60^\circ $ and the little finger denotes $90^\circ $.Let's find out the values if sine. In this method, for sine, count the number of fingers towards the left. Then divide the number by 4 and take the square root of this ratio. For example, for $\sin 0^\circ $, count the number of fingers to the left of the thumb, which is 0. Then divide 0 with four, which is 0. Therefore, $\sin 0^\circ $=0.
Now, we can find other values by using this trick.

Now, by using this table equation (1) becomes,
$
  0 \times \sin 1^\circ \times .......... \times 1 \\
   = 0 \\
 $
Hence, option A is the right answer.

Note – Trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. For solving this question, the different values of the trigonometric ratios must be remembered, for convenience you can draw the table using the trick mentioned above.