Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the ratios of the sides of the triangle. The six main trigonometric ratios are sine, cosine, tangent, cosecant, secant, and cotangent. Let's explain each of these ratios:
1. Sine (sin): The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. It is denoted as sin(theta) or sin(angle).
sin(theta) = opposite/hypotenuse
2. Cosine (cos): The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
cos(theta) = adjacent/hypotenuse
3. Tangent (tan): The tangent of an angle is defined as the ratio of the sine of the angle to the cosine of the angle.
4. Cosecant (csc): The cosecant of an angle is the reciprocal of the sine of the angle.
csc(theta) = 1 / sin(theta) = hypotenuse/opposite
5. Secant (sec): The secant of an angle is the reciprocal of the cosine of the angle.
sec(theta) = 1 / cos(theta) = hypotenuse/adjacent
6. Cotangent (cot): The cotangent of an angle is the reciprocal of the tangent of the angle.
cot(theta) = 1 / tan(theta) = adjacent/opposite
These trigonometric ratios are widely used in mathematics, physics, engineering, and other fields to solve problems involving angles and triangles. They help in calculating unknown angles or side lengths based on the given information.
Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the lengths of its sides. These ratios are commonly used in trigonometry, geometry, and other fields to solve various problems involving angles and distances. The three primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). Additionally, their reciprocals, cosecant (csc), secant (sec), and cotangent (cot), are also commonly used.
1. Sine (sin): The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. It is denoted as sin(θ), where θ represents the angle. Mathematically, sin(θ) = opposite/hypotenuse.
2. Cosine (cos): The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. It is denoted as cos(θ). Mathematically, cos(θ) = adjacent/hypotenuse.
3. Tangent (tan): The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. It is denoted as tan(θ). Mathematically, tan(θ) = opposite/adjacent.
The reciprocals of these ratios are:
4. Cosecant (csc): The cosecant of an angle is the reciprocal of the sine of that angle. It is denoted as csc(θ). Mathematically, csc(θ) = 1/sin(θ) = hypotenuse/opposite.
5. Secant (sec): The secant of an angle is the reciprocal of the cosine of that angle. It is denoted as sec(θ). Mathematically, sec(θ) = 1/cos(θ) = hypotenuse/adjacent.
6. Cotangent (cot): The cotangent of an angle is the reciprocal of the tangent of that angle. It is denoted as cot(θ). Mathematically, cot(θ) = 1/tan(θ) = adjacent/opposite.
These trigonometric ratios can be used to calculate the values of angles and sides in right triangles or to solve various trigonometric equations and problems. They have extensive applications in fields such as physics, engineering, navigation, and more.
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Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the ratios of the sides of the triangle. The six main trigonometric ratios are sine, cosine, tangent, cosecant, secant, and cotangent. Let's explain each of these ratios:
1. Sine (sin): The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. It is denoted as sin(theta) or sin(angle).
sin(theta) = opposite/hypotenuse
2. Cosine (cos): The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
cos(theta) = adjacent/hypotenuse
3. Tangent (tan): The tangent of an angle is defined as the ratio of the sine of the angle to the cosine of the angle.
tan(theta) = sin(theta) / cos(theta) = opposite/adjacent
4. Cosecant (csc): The cosecant of an angle is the reciprocal of the sine of the angle.
csc(theta) = 1 / sin(theta) = hypotenuse/opposite
5. Secant (sec): The secant of an angle is the reciprocal of the cosine of the angle.
sec(theta) = 1 / cos(theta) = hypotenuse/adjacent
6. Cotangent (cot): The cotangent of an angle is the reciprocal of the tangent of the angle.
cot(theta) = 1 / tan(theta) = adjacent/opposite
These trigonometric ratios are widely used in mathematics, physics, engineering, and other fields to solve problems involving angles and triangles. They help in calculating unknown angles or side lengths based on the given information.
Answer:
Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the lengths of its sides. These ratios are commonly used in trigonometry, geometry, and other fields to solve various problems involving angles and distances. The three primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). Additionally, their reciprocals, cosecant (csc), secant (sec), and cotangent (cot), are also commonly used.
1. Sine (sin): The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. It is denoted as sin(θ), where θ represents the angle. Mathematically, sin(θ) = opposite/hypotenuse.
2. Cosine (cos): The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. It is denoted as cos(θ). Mathematically, cos(θ) = adjacent/hypotenuse.
3. Tangent (tan): The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. It is denoted as tan(θ). Mathematically, tan(θ) = opposite/adjacent.
The reciprocals of these ratios are:
4. Cosecant (csc): The cosecant of an angle is the reciprocal of the sine of that angle. It is denoted as csc(θ). Mathematically, csc(θ) = 1/sin(θ) = hypotenuse/opposite.
5. Secant (sec): The secant of an angle is the reciprocal of the cosine of that angle. It is denoted as sec(θ). Mathematically, sec(θ) = 1/cos(θ) = hypotenuse/adjacent.
6. Cotangent (cot): The cotangent of an angle is the reciprocal of the tangent of that angle. It is denoted as cot(θ). Mathematically, cot(θ) = 1/tan(θ) = adjacent/opposite.
These trigonometric ratios can be used to calculate the values of angles and sides in right triangles or to solve various trigonometric equations and problems. They have extensive applications in fields such as physics, engineering, navigation, and more.