Pythagorean Identitiestan²a + 1 =
The Pythagorean Identity is a mathematical equation that relates the trigonometric functions of sine (sin) and cosine (cos)
The Pythagorean Identity is a mathematical equation that relates the trigonometric functions of sine (sin) and cosine (cos).
The correct form of the Pythagorean Identity is:
sin²a + cos²a = 1
This identity holds true for any angle ‘a’ in a right-angled triangle. It states that the square of the sine of an angle added to the square of the cosine of the same angle will always be equal to 1.
If we rearrange the equation, we can see that:
sin²a = 1 – cos²a
Similarly, we can express:
cos²a = 1 – sin²a
These equations allow us to calculate the value of one trigonometric function based on the value of the other. For example, if we know the value of the sine of an angle, we can find the value of the cosine using the Pythagorean Identity.
It is important to note that the Pythagorean Identity is derived from the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. The Pythagorean Identity is a trigonometric extension of this theorem and is widely used in various branches of mathematics and physics.
More Answers:
Exploring the Sum and Difference Identities in Trigonometry | Understanding and Applying Cosine FunctionsUnderstanding the Opposite of Sin(-a) | Exploring the Identity and Unit Circle Explanation
Exploring the Identity for Opposite Cosine (-a) Using the Definition of Cosine Function and Even-Odd Functions