Cofunctions are trigonometric functions that are related by the complementary angles of a right triangle. The complementary angles of a right triangle are two angles whose sum is equal to 90 degrees. In trigonometry, the six primary trigonometric functions are sine, cosine, tangent, cosecant, secant, and cotangent.
When we take the sine of an angle, it is equal to the cosine of the angle's complement. Similarly, when we take the cosine of an angle, it is equal to the sine of the angle's complement. This relationship holds true for all complementary angles.
For example, if angle A is 30 degrees, its complement angle B is 60 degrees. The sine of angle A is 0.5, and the cosine of angle B (the complement of angle A) is also 0.5. Similarly, the cosine of angle A is √3/2, and the sine of angle B (the complement of angle A) is also √3/2.
This is because the sine and cosine functions are defined in terms of the sides of a right triangle and are related by the Pythagorean theorem. Since the complementary angles of a right triangle have the same ratio of sides, their sine and cosine values are the same, just in reverse order. Therefore, cofunctions have the same value because they are related by the complementary angles of a right triangle.
Cofunctions refer to pairs of trigonometric functions that have the same value when their angles are complementary (i.e., they add up to 90 degrees or π/2 radians). The main reason why cofunctions have the same value is rooted in the geometric properties of right triangles.
In a right triangle, the trigonometric functions are defined in terms of the ratios of the sides of the triangle. The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).
When two angles are complementary, their corresponding sides in the right triangle are also complementary. This means that if one angle has a certain ratio of sides for a trigonometric function, the other angle will have the complementary ratio.
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Answer:
Cofunctions are trigonometric functions that are related by the complementary angles of a right triangle. The complementary angles of a right triangle are two angles whose sum is equal to 90 degrees. In trigonometry, the six primary trigonometric functions are sine, cosine, tangent, cosecant, secant, and cotangent.
When we take the sine of an angle, it is equal to the cosine of the angle's complement. Similarly, when we take the cosine of an angle, it is equal to the sine of the angle's complement. This relationship holds true for all complementary angles.
For example, if angle A is 30 degrees, its complement angle B is 60 degrees. The sine of angle A is 0.5, and the cosine of angle B (the complement of angle A) is also 0.5. Similarly, the cosine of angle A is √3/2, and the sine of angle B (the complement of angle A) is also √3/2.
This is because the sine and cosine functions are defined in terms of the sides of a right triangle and are related by the Pythagorean theorem. Since the complementary angles of a right triangle have the same ratio of sides, their sine and cosine values are the same, just in reverse order. Therefore, cofunctions have the same value because they are related by the complementary angles of a right triangle.
Answer:
Cofunctions refer to pairs of trigonometric functions that have the same value when their angles are complementary (i.e., they add up to 90 degrees or π/2 radians). The main reason why cofunctions have the same value is rooted in the geometric properties of right triangles.
In a right triangle, the trigonometric functions are defined in terms of the ratios of the sides of the triangle. The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).
When two angles are complementary, their corresponding sides in the right triangle are also complementary. This means that if one angle has a certain ratio of sides for a trigonometric function, the other angle will have the complementary ratio.
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