Aryabhata, an Indian mathematician and astronomer, is credited with developing the concept of the sine function in the 5th century CE.

The Surya Siddhanta, an Indian treatise on astronomy and mathematics, contains the earliest known description of the astrolabe, a navigational instrument used to measure the altitude of celestial bodies.

Aryabhata developed a method for calculating the circumference of the Earth using trigonometry in the 5th century CE.

Brahmagupta, an Indian mathematician and astronomer, developed a method for calculating the position of a ship at sea using the stars in the 7th century CE.

Aryabhata developed a method for calculating the time of sunrise and sunset using trigonometry in the 5th century CE.

The Panchasiddhantika, an Indian treatise on navigation, contains instructions for using the astrolabe and other navigational instruments.

Brahmagupta developed a method for calculating the distance between two ships at sea using trigonometry in the 7th century CE.

Brahmagupta developed a method for calculating the speed of a ship at sea using trigonometry in the 7th century CE.

Brahmagupta developed a method for calculating the direction of a ship at sea using trigonometry in the 7th century CE.

The Panchasiddhantika, an Indian treatise on navigation, contains instructions for using the compass.

Brahmagupta developed a method for calculating the latitude of a ship at sea using the stars in the 7th century CE.

The Panchasiddhantika, an Indian treatise on navigation, contains instructions for using the quadrant.

Brahmagupta developed a method for calculating the longitude of a ship at sea using the stars in the 7th century CE.

The Panchasiddhantika, an Indian treatise on navigation, contains instructions for using the backstaff.

Aryabhata developed a method for calculating the declination of the sun using trigonometry in the 5th century CE.