Question

What is the value of \[\sin {{37}^{\circ }}34'\] to four decimal places?

Answer 1

Hint: In this problem we have to find out the value of the given trigonometric function , \[\sin {{37}^{\circ }}34'\]. From the given data \[\sin {{37}^{\circ }}34'\] first we can consider the part \[34'\]. We know that one degree consists of 60 minutes. We can divide the minutes to 60, to convert it. Then with the help of a scientific calculator we can find the value of the above trigonometrical term.

Complete step-by-step solution:
Here we have to find the value of \[\sin {{37}^{\circ }}34'\]
From the given data \[\sin {{37}^{\circ }}34'\] first we can consider the part \[34'\],
\[\Rightarrow 34'\]
We know that one degree consists of 60 minutes. So,
\[\Rightarrow 34'=\dfrac{34}{60}\]
Now we can simplify, it we get
\[\Rightarrow 34'=\dfrac{17}{30}\]
Now simplifying this fractional into decimal form we get,
\[\Rightarrow 34'=0.5667\]
We have one thing here to remember we have just simplified one part of the trigonometric function, hence now we can add this decimal value with the angle of the trigonometric function
\[\Rightarrow {{37.5667}^{\circ }}\]
Hence,
\[\Rightarrow \sin {{37.5667}^{\circ }}\]
Now with the help of a scientific calculator we can find the value of the above trigonometrical term, we get
\[\Rightarrow \sin {{37.5667}^{\circ }}=0.60968\]
In this problem here we are asked to find out only four digits after the decimal, so rounding off it and we get an approximate value,
\[\Rightarrow \sin {{37.5667}^{\circ }}\cong 0.6097\]
Therefore, the solution \[\sin {{37}^{\circ }}34'\approx 0.6097\].

Note: This trigonometrical value can be solved through another method also by using the tables of sine charts. While using sine chart in against of \[{{37}^{\circ }}\]we have to pick \[34'\] but sine chart may not consist of \[34'\], so instead of \[34'\] we can pick \[30'\]and we get a value. Now pick the number under \[4'\], now we can add this number with the value we already pick with \[30'\]. And now we can get the same value as how we solved this. But while using a sine chart we should be careful while picking the values.