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Question: Find \( \sin 36^\circ 51'. \) A. \( 0.677 \) B. \( 0.999 \) C. \( 0.238 \) D. \( 0.599 \...

Find sin⁡36∘51′.\sin 36^\circ 51'.
A. 0.6770.677
B. 0.9990.999
C. 0.2380.238
D. 0.5990.599

Explanation

Solution

Hint : To find the values of the given sine function, here we will use log table. It is used to find the value of the logarithmic function. Before the invention of the computers and other electronic devices, this log book was widely used and the easier way to get the required answer. It contains values for logarithms, antilogarithms, and tangent, sine and cosine functions. So, go to the page having values for the sine functions.

Complete step-by-step answer :
Refer to the natural sine functions page in the log book.
First column represents the degree of the sine functions. In the rest columns we have minutes such as 0′,6′,12′,18′,24′,30′,36′,42′,48′,54′0',6',12',18',24',30',36',42',48',54' and the last few columns are the mean difference represents minutes such as 1′,2′,3′,4′,5′1',2',3',4',5'
Now, look for the given angles.
First for the degree angle 36∘36^\circ then go horizontally to find the value of minutes in it.
Here we are given the minutes 51′51' , which is not directly given. To make it add the values of 36∘48′+3′36^\circ 48' + 3'
Now, Note the value of 36∘48′=0.599036^\circ 48' = 0.5990
And add the Value of 3′=73' = 7
⇒sin⁡(36∘51′)=0.5997\Rightarrow \sin (36^\circ 51') = 0.5997
Hence, from the given multiple choices – the option A is the correct answer.
So, the correct answer is “Option D”.

Note : Always double check for the page, and the function for which you are looking. Use scale to refer and go through the horizontal lines for the required values for the minutes. Since, a log book is a series of the numbers, observe and note the given number carefully and always cross-check it.