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Bhaskara II's Contributions to Trigonometry and Calculus

Description: Bhaskara II was an Indian mathematician and astronomer who lived in the 12th century. He is considered to be one of the greatest mathematicians of his time, and his work had a profound influence on the development of mathematics in India and beyond. This quiz will test your knowledge of Bhaskara II's contributions to trigonometry and calculus.
Number of Questions: 15
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Tags: bhaskara ii trigonometry calculus indian mathematics
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What is the name of the treatise written by Bhaskara II that contains his work on trigonometry and calculus?

  1. Lilavati

  2. Bijaganita

  3. Siddhanta Shiromani

  4. Karanakutuhala


Correct Option: C
Explanation:

The Siddhanta Shiromani is a comprehensive treatise on astronomy and mathematics written by Bhaskara II in the 12th century. It consists of four parts, one of which is devoted to trigonometry and calculus.

What is the formula for the sine of an angle in a right triangle, as given by Bhaskara II?

  1. $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$

  2. $\sin \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$

  3. $\sin \theta = \frac{\text{opposite}}{\text{adjacent}}$

  4. $\sin \theta = \frac{\text{hypotenuse}}{\text{adjacent}}$


Correct Option: A
Explanation:

Bhaskara II's formula for the sine of an angle is $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$. This formula is still used today in trigonometry.

What is the formula for the cosine of an angle in a right triangle, as given by Bhaskara II?

  1. $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$

  2. $\cos \theta = \frac{\text{opposite}}{\text{hypotenuse}}$

  3. $\cos \theta = \frac{\text{opposite}}{\text{adjacent}}$

  4. $\cos \theta = \frac{\text{hypotenuse}}{\text{adjacent}}$


Correct Option: A
Explanation:

Bhaskara II's formula for the cosine of an angle is $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$. This formula is still used today in trigonometry.

What is the formula for the tangent of an angle in a right triangle, as given by Bhaskara II?

  1. $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$

  2. $\tan \theta = \frac{\text{adjacent}}{\text{opposite}}$

  3. $\tan \theta = \frac{\text{hypotenuse}}{\text{opposite}}$

  4. $\tan \theta = \frac{\text{hypotenuse}}{\text{adjacent}}$


Correct Option: A
Explanation:

Bhaskara II's formula for the tangent of an angle is $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$. This formula is still used today in trigonometry.

What is the formula for the area of a triangle, as given by Bhaskara II?

  1. $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

  2. $\text{Area} = \frac{1}{2} \times \text{base} \times \text{side}$

  3. $\text{Area} = \frac{1}{2} \times \text{side} \times \text{height}$

  4. $\text{Area} = \frac{1}{2} \times \text{side} \times \text{side}$


Correct Option: A
Explanation:

Bhaskara II's formula for the area of a triangle is $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$. This formula is still used today in geometry.

What is the formula for the volume of a sphere, as given by Bhaskara II?

  1. $\text{Volume} = \frac{4}{3} \times \pi \times \text{radius}^3$

  2. $\text{Volume} = \frac{3}{4} \times \pi \times \text{radius}^3$

  3. $\text{Volume} = \frac{1}{3} \times \pi \times \text{radius}^3$

  4. $\text{Volume} = \frac{2}{3} \times \pi \times \text{radius}^3$


Correct Option: A
Explanation:

Bhaskara II's formula for the volume of a sphere is $\text{Volume} = \frac{4}{3} \times \pi \times \text{radius}^3$. This formula is still used today in geometry.

What is the formula for the circumference of a circle, as given by Bhaskara II?

  1. $\text{Circumference} = \pi \times \text{diameter}$

  2. $\text{Circumference} = 2 \times \pi \times \text{radius}$

  3. $\text{Circumference} = \pi \times \text{radius}$

  4. $\text{Circumference} = 2 \times \pi \times \text{diameter}$


Correct Option: B
Explanation:

Bhaskara II's formula for the circumference of a circle is $\text{Circumference} = 2 \times \pi \times \text{radius}$. This formula is still used today in geometry.

What is the formula for the area of a circle, as given by Bhaskara II?

  1. $\text{Area} = \pi \times \text{radius}^2$

  2. $\text{Area} = 2 \times \pi \times \text{radius}^2$

  3. $\text{Area} = \frac{1}{2} \times \pi \times \text{radius}^2$

  4. $\text{Area} = \frac{1}{4} \times \pi \times \text{radius}^2$


Correct Option: A
Explanation:

Bhaskara II's formula for the area of a circle is $\text{Area} = \pi \times \text{radius}^2$. This formula is still used today in geometry.

What is the formula for the sum of the first n natural numbers, as given by Bhaskara II?

  1. $\text{Sum} = \frac{n(n+1)}{2}$

  2. $\text{Sum} = \frac{n(n-1)}{2}$

  3. $\text{Sum} = \frac{n(n+2)}{2}$

  4. $\text{Sum} = \frac{n(n-2)}{2}$


Correct Option: A
Explanation:

Bhaskara II's formula for the sum of the first n natural numbers is $\text{Sum} = \frac{n(n+1)}{2}$. This formula is still used today in mathematics.

What is the formula for the product of the first n natural numbers, as given by Bhaskara II?

  1. $\text{Product} = n!$

  2. $\text{Product} = (n+1)!$

  3. $\text{Product} = (n-1)!$

  4. $\text{Product} = (n+2)!$


Correct Option: A
Explanation:

Bhaskara II's formula for the product of the first n natural numbers is $\text{Product} = n!$. This formula is still used today in mathematics.

What is the formula for the nth Fibonacci number, as given by Bhaskara II?

  1. $\text{F}_n = \frac{\sqrt{5}}{5} \left[\left(\frac{1+\sqrt{5}}{2}\right)^n - \left(\frac{1-\sqrt{5}}{2}\right)^n\right]$

  2. $\text{F}_n = \frac{\sqrt{5}}{5} \left[\left(\frac{1+\sqrt{5}}{2}\right)^n + \left(\frac{1-\sqrt{5}}{2}\right)^n\right]$

  3. $\text{F}_n = \frac{\sqrt{5}}{5} \left[\left(\frac{1+\sqrt{5}}{2}\right)^n \times \left(\frac{1-\sqrt{5}}{2}\right)^n\right]$

  4. $\text{F}_n = \frac{\sqrt{5}}{5} \left[\left(\frac{1+\sqrt{5}}{2}\right)^n \div \left(\frac{1-\sqrt{5}}{2}\right)^n\right]$


Correct Option: A
Explanation:

Bhaskara II's formula for the nth Fibonacci number is $\text{F}_n = \frac{\sqrt{5}}{5} \left[\left(\frac{1+\sqrt{5}}{2}\right)^n - \left(\frac{1-\sqrt{5}}{2}\right)^n\right]$. This formula is still used today in mathematics.

What is the formula for the area of a parallelogram, as given by Bhaskara II?

  1. $\text{Area} = \text{base} \times \text{height}$

  2. $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

  3. $\text{Area} = 2 \times \text{base} \times \text{height}$

  4. $\text{Area} = \frac{1}{4} \times \text{base} \times \text{height}$


Correct Option: A
Explanation:

Bhaskara II's formula for the area of a parallelogram is $\text{Area} = \text{base} \times \text{height}$. This formula is still used today in geometry.

What is the formula for the volume of a rectangular prism, as given by Bhaskara II?

  1. $\text{Volume} = \text{length} \times \text{width} \times \text{height}$

  2. $\text{Volume} = 2 \times \text{length} \times \text{width} \times \text{height}$

  3. $\text{Volume} = \frac{1}{2} \times \text{length} \times \text{width} \times \text{height}$

  4. $\text{Volume} = \frac{1}{4} \times \text{length} \times \text{width} \times \text{height}$


Correct Option: A
Explanation:

Bhaskara II's formula for the volume of a rectangular prism is $\text{Volume} = \text{length} \times \text{width} \times \text{height}$. This formula is still used today in geometry.

What is the formula for the volume of a pyramid, as given by Bhaskara II?

  1. $\text{Volume} = \frac{1}{3} \times \text{base area} \times \text{height}$

  2. $\text{Volume} = \frac{1}{2} \times \text{base area} \times \text{height}$

  3. $\text{Volume} = \frac{2}{3} \times \text{base area} \times \text{height}$

  4. $\text{Volume} = \frac{3}{4} \times \text{base area} \times \text{height}$


Correct Option: A
Explanation:

Bhaskara II's formula for the volume of a pyramid is $\text{Volume} = \frac{1}{3} \times \text{base area} \times \text{height}$. This formula is still used today in geometry.

What is the formula for the volume of a cone, as given by Bhaskara II?

  1. $\text{Volume} = \frac{1}{3} \times \pi \times \text{radius}^2 \times \text{height}$

  2. $\text{Volume} = \frac{1}{2} \times \pi \times \text{radius}^2 \times \text{height}$

  3. $\text{Volume} = \frac{2}{3} \times \pi \times \text{radius}^2 \times \text{height}$

  4. $\text{Volume} = \frac{3}{4} \times \pi \times \text{radius}^2 \times \text{height}$


Correct Option: A
Explanation:

Bhaskara II's formula for the volume of a cone is $\text{Volume} = \frac{1}{3} \times \pi \times \text{radius}^2 \times \text{height}$. This formula is still used today in geometry.

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