Why trigonometric ratios were defined for a unit circle

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Thread starter prashant singh
Start date Apr 27, 2016
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Circle Ratios Trigonometric Unit Unit circle

In summary, trigonometric ratios were defined for a unit circle to provide a standard reference point for measuring angles. These ratios are related to the unit circle as they are calculated based on the measurements of sides of a right triangle within it. While they can be used with any circle, the unit circle is preferred for its simplicity and accuracy. The unit circle is used in trigonometry as it visually represents the relationship between angles and ratios and allows for easier calculations. Additionally, the unit circle relates to the Pythagorean theorem as it is essentially a right triangle with sides of 1 unit, allowing for the calculation of the hypotenuse, which is needed for trigonometric ratios.

Apr 27, 2016

prashant singh

To make it useful for any angles. I need a good explanation for this.

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Apr 27, 2016

jedishrfu

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Think about the advantage of having a circle of radius 1. What does the sin and cos of any angle reduce to?

Apr 27, 2016

prashant singh

Y and x okkk ,

1. Why were trigonometric ratios defined for a unit circle?

Trigonometric ratios were defined for a unit circle because it provides a standard reference point for measuring angles. The radius of a unit circle is always 1 unit, making it easier to compare and calculate ratios between different angles.

2. How are trigonometric ratios related to a unit circle?

Trigonometric ratios, such as sine, cosine, and tangent, are calculated based on the measurements of sides of a right triangle within the unit circle. This allows for a consistent and reliable way to calculate these ratios for any angle.

3. Can trigonometric ratios be used with any circle?

Yes, trigonometric ratios can be used with any circle. However, using a unit circle as a reference point simplifies the calculations and provides more accurate results.

4. Why is the unit circle used in trigonometry?

The unit circle is used in trigonometry because it provides a visual representation of the relationship between angles and trigonometric ratios. It also allows for easier calculation and comparison of these ratios for different angles.

5. How does the unit circle relate to the Pythagorean theorem?

The unit circle relates to the Pythagorean theorem because it is essentially a right triangle with sides of 1 unit. This means that the Pythagorean theorem can be used to calculate the length of the hypotenuse, which is necessary for calculating trigonometric ratios.