
Find the value of in terms of fraction.
Answer
393.9k+ views
Hint: In this question, we have to write the given trigonometric function in terms of fraction.
We know, that in a right- angled triangle, there are three sides, perpendicular, base and the hypotenuse.
And, , where, is the length of perpendicular and is referred to as the length of hypotenuse, whereas, , where, is the length of perpendicular and is the length of base of the triangle.
Complete answer:
Given trigonometric functions .
To write these trigonometric functions in terms of fraction.
Consider a right- angled triangle, , with and .
Then, we have, using angle sum property of a triangle, that, , i.e., . On solving, we get, i.e., .
Now, let length of side is and length of side is , then, by Pythagoras theorem, we have, , putting values, we get, , hence, .
Now, we know, , and for angle , and . So, .
Similarly, for angle , and . So, .
Now, for angle , and . So, .
Similarly, for angle , and . So,
Note:
It is not necessary to choose the lengths of sides of the triangle to be or . We can choose the length of sides of the right- angled triangle by our choices.
If , then, taking square root on both sides, we get, , but in this question, we are talking about length of sides and length can never be negative. Hence, we have taken only the positive one.
For any angle, say , the sides opposite to this angle will be the perpendicular side, whereas, the third side except for the hypotenuse, will be the base of the triangle.
We know, that in a right- angled triangle, there are three sides, perpendicular, base and the hypotenuse.
And,
Complete answer:
Given trigonometric functions
To write these trigonometric functions in terms of fraction.
Consider a right- angled triangle,

Then, we have, using angle sum property of a triangle, that,
Now, let length of side
Now, we know,
Similarly, for angle
Now, for angle
Similarly, for angle
Note:
It is not necessary to choose the lengths of sides of the triangle to be
If
For any angle, say
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