the value of sin a and cos a never be greater than 1 true or false
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The value of $\\sin A$ or $\\cos A$ never exceeds the value_____.
The value of $\\sin A$ or $\\cos A$ never exceeds the value_____.. Ans: Hint: First use the trigonometric ratio to find the ratio of sine and cosine in terms of perpendicular, base and hypotenuse. Then use the Pythagoras theorem to get the result tha...
The value ofsinA sinA or cosA cosA
never exceeds the value_____.
Last updated date: 11th Mar 2023
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Hint: First use the trigonometric ratio to find the ratio of sine and cosine in terms of perpendicular, base and hypotenuse. Then use the Pythagoras theorem to get the result that the Hypotenuse is the longest side of the right triangle. Use this result to get the desired result.Complete step-by-step answer:For any right angle triangle, which is right-angled at angle B. Then for the angle A, the base of the triangle is AB, perpendicular to the triangle is BC, and the hypotenuse of the triangle is AC. The figure of the triangle is shown.
Using the trigonometric ratios, we know that the sine of the angle A is the ratio of the perpendicular and the hypotenuse and cosine is the ratio of the base and the hypotenuse. That is,
sinA= Perpendicular Hypotenuse
sinA=PerpendicularHypotenuse
cosA= Base Hypotenuse
cosA=BaseHypotenuse
Using the Pythagoras theorem, the square of the hypotenuse of the triangle is equal to the sum of the square of the perpendicular and the base of the triangle.
(Hypotenuse) 2 = (Perpendicular) 2 + (Base) 2
(Hypotenuse)2=(Perpendicular)2+(Base)2
Then we can conclude that:
(Hypotenuse) 2 > (Perpendicular) 2
(Hypotenuse)2>(Perpendicular)2
and (Hypotenuse) 2 > (Base) 2
(Hypotenuse)2>(Base)2
⇒Hypotenuse>Perpendicular
⇒Hypotenuse>Perpendicular
and Hypotenuse>Base Hypotenuse>Base
So, we get the conclusion that the hypotenuse of the right triangle is the longest side of the triangle.
Thus, the ratio of sine and cosine is always less than 1.
So, the value ofsinA sinA or cosA cosA
never exceeds the value 1.
Note: While using the Pythagoras theorem, remember that the perpendicular and the base of the triangle are changed with the angle. We have used angle A for finding the ratio of the sine and cosine. In case, if we use the angle C, then the perpendicular is taken as AB and base is taken as BC.
the value of sin a and cos a never be greater than 1
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March 18, 2023
THE VALUE OF SIN A AND COS A NEVER BE GREATER THAN 1
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Click here to get an answer to your question ️ 5. The value of sin A or cos A never exceeds ( 1 , ) whereas the value of ( sec A ) always greater than or equal to ( 1 .
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Answer (1 of 4): sine=frac{opposite}{hypotenuse} cosine=frac{adjacent}{hypotenuse} The hypotenuse will always have a larger measure than the opposite and adjacent in a right-angled triangle, therefore, the sine and cosine is never greater than 1.
What is trigonometry – Can the value of sin theta be greater than 1
We know that the Hypotenuse is never shorter than the line Opposite the angle $theta$, so this fraction can never exceed $1$. So if $theta$ is complex, then it can exceed $1$.
Why can sine and cosine ratios never be greater than 1. The simple reason is that the length of the sides of a right triangle are always less than the length of the hypotenuse.
How to use The value of sinθ + cosθ is always greater than 1. Write ‘True’ or
Given, the statement is “the value of sinθ + cosθ is always greater than 1”. We have to determine if the given statement is true or false.
The values of sin and cos becomes less than 1 because When we divide the leg and hypotenuse we get smaller value than 1 The value of cosec and sec becomes greater than 1 because cosecant function always produces values bigger than 1. Stp-by-step explanation: Given that the values of sin and cos never exceed one.
Answer (1 of 8): Coine is a trigonometric function and it is defined as the ratio of base to the hypotenuse of a right triangle. Because the Pythagoras theorem says, (Hypotenuse)^2=(base)^2+(perpendicular)^2 And we assume the case where none of the quantities above is zero(if any one of them.
Answer (1 of 3): I will give you the most useful answer I can, the same answer I give to any student who asks this kind of question: Try to break the rule. I assume you are in the universe of right triangles or you would have already encountered the lower limit of -1.
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The value of sinθ + cosθ is always greater than 1. Write ‘True’ or ‘False’ and justify your answer
The value of sinθ + cosθ is always greater than 1. Write ‘True’ or ‘False’ and justify your answer - The sine of an angle is the ratio of the opposite side and the hypotenuse and the cosine of an angle
The value of sinθ + cosθ is always greater than 1. Write ‘True’ or ‘False’ and justify your answer
Solution:Given, the statement is “the value of sinθ + cosθ is always greater than 1”
We have to determine if the given statement is true or false.
θ 0° 30° 45° 60° 90° sinθ 0 1/2 1/√2 √3/2 1 cosθ 1 √3/2 1/√2 1/2 0
By using trigonometric ratio of angles,
Sin 0° + cos 90° = 0 + 0 = 0
sin 90° + cos 90° = 1 + 0 = 1 which is not greater than one.
Therefore, the value of sinθ + cosθ is always greater than 1 is false.
✦ Try This: If tan A = a/b then (cos A - sin A)/(cos A + sin A) = ?Given, tan A = a/b
We have to find (cos A - sin A)/(cos A + sin A)
Dividing numerator and denominator by cos A,
= (1 - sin A/cos A)/(1 + sin A/cos A)
= (1 - tan A)/(1 + tan A)
= (1 - a/b)/(1 + a/b)
= (b - a)/b / (b + a)/b
= (b - a)/(b + a)
Therefore, (cos A - sin A)/(cos A + sin A)= (b - a)/(b + a)
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8NCERT Exemplar Class 10 Maths Exercise 8.2 Sample Problem 1The value of sinθ + cosθ is always greater than 1. Write ‘True’ or ‘False’ and justify your answer
Summary:The sine of an angle is the ratio of the opposite side and the hypotenuse and the cosine of an angle is the ratio of the adjacent side and the hypotenuse. The statement “The value of sinθ + cosθ is always greater than 1” is false
☛ Related Questions:The value of tanθ (θ < 90°) increases as θ increases. Write ‘True’ or ‘False’ and justify your answe . . . .
tanθ increases faster than sinθ as θ increases. Write ‘True’ or ‘False’ and justify your answer
The value of sinθ is a+(1/a), where ‘a’ is a positive number. Write ‘True’ or ‘False’ and justify y . . . .
Guys, does anyone know the answer?