Question

How do you use a calculator to evaluate \[\sin 4\]?

Answer 1

Hint: The functions sine, cosine and tangent of an angle are sometimes referred to as the primary or basic trigonometric functions. Trigonometric identities are the equations involving the trigonometric functions that are true for every value of the variables involved.

Complete step by step answer:
As per the given question, we need to find the value of \[\sin 4\] using a calculator. It is better to use a scientific calculator than a normal calculator since it gives accurate values for complex functions and has more functions to solve complex problems.
Firstly, on the calculator and then press the button \[''\sin ''\] then enter the value 4. Now press the button “Ans” to get the value.
The calculator shows the value of \[\sin 4\]as follows:
\[\sin 4=-0.756802495\]
Here, we consider 4 in radians and not in degrees because in the question it is not mentioned in degrees \[''\circ ''\].
The value of \[''\sin ''\] is negative in \[{{3}^{rd}}and{{4}^{th}}\] quadrant.
We can find the value of \[\sin 4\] without using a calculator by converting it into degrees and finding the value.
\[1radian={{57.2958}^{\circ }}\].
By using the above relation, we can convert radians to degrees.

Therefore, the value of \[\sin 4\] is \[-0.756802495\].

Note: In order to solve such types of questions, we need to have enough knowledge over trigonometric functions, identities and their properties. We must check whether the value given is in radians or degrees. We also need to know the algebraic formulae to simplify the expressions. We must avoid calculation mistakes to get the expected answers.