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Question: The value of \[{\text{sin 9}}{{\text{0}}^{\text{0}}}{\text{}}\] is ________ A. \[0\] B. \[1\] ...

The value of sin 900{\text{sin 9}}{{\text{0}}^{\text{0}}}{\text{}} is ________
A. 00
B. 11
C. 12\dfrac{1}{2}
D. 32\dfrac{{\sqrt 3 }}{2}

Explanation

Solution

Hint:

To find out the value of sin 900{\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⁡θ=y1\sin\theta = \dfrac{{\text{y}}}{{\text{1}}}
Start measuring the angles from the first quadrant and end up with 900  {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.
sinθ=y1 = 11sin\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  11{\text{ }}\dfrac{1}{1}. Hence sin 900{\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 sin 900{\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.