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Why does sin 90 degrees equal 1? We know that formula for sin is perpendicular upon hypotenuse where hypotenuse is longest side?
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Why does sin 90 degrees equal 1? We know that formula for sin is perpe...
As shown above, In a right triangle ABC right angled at B , <A = pound sign
& sin pound sign = opposite side / hypotenuse = BC/ AC
Now in the triangle ABC, as AC is rotated anticlockwise for converting < pound sign = 90degree, BC comes closer to AC & Base AB gradually becomes shorter. Finally when this acute angle pound sign is converted into 90degree ,
BC coincides with AC ie AC = BC & AB = 0
ie , hypotenuse = perpendicular ( opposite side) & Base = 0
So, sin 90degree = perpendicular/ hypotenuse = 1 : 1
=> sin 90degree= 1
This question is part of UPSC exam. View all Class 10 courses
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Why does sin 90 degrees equal 1? We know that formula for sin is perpe...
Explanation of why sin 90 degrees equals 1:
- Definition of sin:
The sine of an angle in a right triangle is defined as the length of the side opposite the angle divided by the length of the hypotenuse.
- Understanding a 90-degree angle:
In a right triangle with a 90-degree angle, the side opposite the 90-degree angle is the side opposite the right angle, which is the longest side of the triangle, also known as the hypotenuse.
- Calculating sin 90 degrees:
When we calculate sin 90 degrees, we are essentially taking the length of the side opposite the angle (which is the length of the hypotenuse) and dividing it by the length of the hypotenuse itself.
Mathematically, sin 90 degrees = (length of hypotenuse) / (length of hypotenuse) = 1.
- Visual representation:
Visually, in a right triangle with a 90-degree angle, the length of the side opposite the right angle (the hypotenuse) is the same as the length of the hypotenuse itself. This is why sin 90 degrees equals 1.
Therefore, sin 90 degrees equals 1 because in a right triangle with a 90-degree angle, the side opposite the angle (the hypotenuse) is the longest side, and when we apply the definition of sin, we find that the sine of 90 degrees is 1.
- Definition of sin:
The sine of an angle in a right triangle is defined as the length of the side opposite the angle divided by the length of the hypotenuse.
- Understanding a 90-degree angle:
In a right triangle with a 90-degree angle, the side opposite the 90-degree angle is the side opposite the right angle, which is the longest side of the triangle, also known as the hypotenuse.
- Calculating sin 90 degrees:
When we calculate sin 90 degrees, we are essentially taking the length of the side opposite the angle (which is the length of the hypotenuse) and dividing it by the length of the hypotenuse itself.
Mathematically, sin 90 degrees = (length of hypotenuse) / (length of hypotenuse) = 1.
- Visual representation:
Visually, in a right triangle with a 90-degree angle, the length of the side opposite the right angle (the hypotenuse) is the same as the length of the hypotenuse itself. This is why sin 90 degrees equals 1.
Therefore, sin 90 degrees equals 1 because in a right triangle with a 90-degree angle, the side opposite the angle (the hypotenuse) is the longest side, and when we apply the definition of sin, we find that the sine of 90 degrees is 1.
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Why does sin 90 degrees equal 1? We know that formula for sin is perpendicular upon hypotenuse where hypotenuse is longest side?
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Why does sin 90 degrees equal 1? We know that formula for sin is perpendicular upon hypotenuse where hypotenuse is longest side? 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 Why does sin 90 degrees equal 1? We know that formula for sin is perpendicular upon hypotenuse where hypotenuse is longest side? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Why does sin 90 degrees equal 1? We know that formula for sin is perpendicular upon hypotenuse where hypotenuse is longest side?.
Why does sin 90 degrees equal 1? We know that formula for sin is perpendicular upon hypotenuse where hypotenuse is longest side? 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 Why does sin 90 degrees equal 1? We know that formula for sin is perpendicular upon hypotenuse where hypotenuse is longest side? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Why does sin 90 degrees equal 1? We know that formula for sin is perpendicular upon hypotenuse where hypotenuse is longest side?.
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