Question

The value of \[{\text{sin 9}}{{\text{0}}^{\text{0}}}{\text{}}\] is ________
A. \[0\]
B. \[1\]
C. \[\dfrac{1}{2}\]
D. \[\dfrac{{\sqrt 3 }}{2}\]

Answer 1

Hint:

To find out the value of \[{\text{sin 9}}{{\text{0}}^{\text{0}}}{\text{}}\], we can draw a circle as shown above. From this circle and with the basic knowledge of trigonometry, we can conclude that, for the given right-angled triangle with perpendicular measuring ‘y’ units and its base measuring ‘x’ units.

Complete step-by-step answer:
We know that,
For any right-angled triangle measuring with any of the angles, sine functions equal to the ratio of the length of the opposite side to the length of the hypotenuse side. So, from the figure
\[\sin\theta = \dfrac{{\text{y}}}{{\text{1}}}\]
Start measuring the angles from the first quadrant and end up with \[{90^0}\;\]when it reaches the positive y axis. Now the value of y becomes 1 since it touches the circumference of the circle. Therefore, the value of y becomes 1.
\[sin\theta = \dfrac{{\text{y}}}{{\text{1}}}{\text{ = }}\dfrac{{\text{1}}}{{\text{1}}}\]
From the above explanation it is clear that Sin 90 degree equals to the fractional value of \[{\text{ }}\dfrac{1}{1}\]. Hence \[{\text{sin 9}}{{\text{0}}^{\text{0}}}{\text{}}\]= 1.

Note: Whenever we come up with the type of problem where we asked to find the value of \[{\text{sin 9}}{{\text{0}}^{\text{0}}}{\text{}}\]it is wise to draw a circle which helps us to understand the given situation more practically. Thus, it will help us to find the correct and required answer.