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Given tanA=4/3,find the other trigonometric ratios of the angle A.
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Given tanA=4/3,find the other trigonometric ratios of the angle A.
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Given tanA=4/3,find the other trigonometric ratios of the angle A.
Trigonometric Ratios of Angle A:
To find the other trigonometric ratios of angle A, given that tan A = 4/3, we can use the trigonometric definitions and relationships between the trigonometric functions. The tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
1. Find the values of sin A, cos A, cot A, sec A, and csc A:
To find the values of sin A, cos A, cot A, sec A, and csc A, we can use the following relationships:
1.1. Sine (sin): The sine of an angle A is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.
1.2. Cosine (cos): The cosine of an angle A is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
1.3. Cotangent (cot): The cotangent of an angle A is defined as the reciprocal of the tangent of angle A, which is equal to 1 divided by tan A.
1.4. Secant (sec): The secant of an angle A is defined as the reciprocal of the cosine of angle A, which is equal to 1 divided by cos A.
1.5. Cosecant (csc): The cosecant of an angle A is defined as the reciprocal of the sine of angle A, which is equal to 1 divided by sin A.
2. Calculation:
2.1. Sine (sin A): To find sin A, we can use the Pythagorean theorem, as sin A = opposite/hypotenuse. Let's assume the opposite side length as 4 units and the adjacent side length as 3 units. Using the Pythagorean theorem, we can calculate the hypotenuse (h):
h^2 = 3^2 + 4^2
h^2 = 9 + 16
h^2 = 25
h = √25
h = 5
Therefore, sin A = 4/5.
2.2. Cosine (cos A): To find cos A, we can use the Pythagorean theorem, as cos A = adjacent/hypotenuse. Using the given lengths of the adjacent and opposite sides, we can calculate cos A:
cos A = 3/5
2.3. Cotangent (cot A): To find cot A, we can use the reciprocal of the tangent function, as cot A = 1/tan A:
cot A = 1/(4/3)
cot A = 3/4
2.4. Secant (sec A): To find sec A, we can use the reciprocal of the cosine function, as sec A = 1/cos A:
sec A = 1/(3/5)
sec A = 5/3
2.5. C
To find the other trigonometric ratios of angle A, given that tan A = 4/3, we can use the trigonometric definitions and relationships between the trigonometric functions. The tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
1. Find the values of sin A, cos A, cot A, sec A, and csc A:
To find the values of sin A, cos A, cot A, sec A, and csc A, we can use the following relationships:
1.1. Sine (sin): The sine of an angle A is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.
1.2. Cosine (cos): The cosine of an angle A is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
1.3. Cotangent (cot): The cotangent of an angle A is defined as the reciprocal of the tangent of angle A, which is equal to 1 divided by tan A.
1.4. Secant (sec): The secant of an angle A is defined as the reciprocal of the cosine of angle A, which is equal to 1 divided by cos A.
1.5. Cosecant (csc): The cosecant of an angle A is defined as the reciprocal of the sine of angle A, which is equal to 1 divided by sin A.
2. Calculation:
2.1. Sine (sin A): To find sin A, we can use the Pythagorean theorem, as sin A = opposite/hypotenuse. Let's assume the opposite side length as 4 units and the adjacent side length as 3 units. Using the Pythagorean theorem, we can calculate the hypotenuse (h):
h^2 = 3^2 + 4^2
h^2 = 9 + 16
h^2 = 25
h = √25
h = 5
Therefore, sin A = 4/5.
2.2. Cosine (cos A): To find cos A, we can use the Pythagorean theorem, as cos A = adjacent/hypotenuse. Using the given lengths of the adjacent and opposite sides, we can calculate cos A:
cos A = 3/5
2.3. Cotangent (cot A): To find cot A, we can use the reciprocal of the tangent function, as cot A = 1/tan A:
cot A = 1/(4/3)
cot A = 3/4
2.4. Secant (sec A): To find sec A, we can use the reciprocal of the cosine function, as sec A = 1/cos A:
sec A = 1/(3/5)
sec A = 5/3
2.5. C
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Given tanA=4/3,find the other trigonometric ratios of the angle A.
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Given tanA=4/3,find the other trigonometric ratios of the angle A. for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Given tanA=4/3,find the other trigonometric ratios of the angle A. covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given tanA=4/3,find the other trigonometric ratios of the angle A..
Given tanA=4/3,find the other trigonometric ratios of the angle A. for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Given tanA=4/3,find the other trigonometric ratios of the angle A. covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given tanA=4/3,find the other trigonometric ratios of the angle A..
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