हिंदी

The maximum distance of a point on the graph of the function y = 3 sinx + cosx from x-axis is ______. - Mathematics

Advertisements
Advertisements

प्रश्न

The maximum distance of a point on the graph of the function y = `sqrt(3)` sinx + cosx from x-axis is ______.

रिक्त स्थान भरें

उत्तर

The maximum distance of a point on the graph of the function y = `sqrt(3)` sinx + cosx from x-axis is 2.

Explanation:

Given that y = `sqrt(3)` sinx + cosx  .......(i)

∴ The maximum distance from a point on the graph of equation (i) from x-axis

= `sqrt((sqrt(3))^2 + (1)^2`

= `sqrt(3 + 1)`

= 2

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Trigonometric Functions - Exercise [पृष्ठ ६०]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 3 Trigonometric Functions
Exercise | Q 67 | पृष्ठ ६०

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Prove the following: `cos (pi/4 xx x) cos (pi/4 - y) - sin (pi/4 -  x)sin (pi/4  - y) =  sin (x + y)`


Prove the following: `(tan(pi/4 + x))/(tan(pi/4 - x)) = ((1+ tan x)/(1- tan x))^2`


Prove the following:

cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x) 


Prove the following:

cos 4x = 1 – 8sinx cosx


Prove that: `((sin 7x + sin 5x) + (sin 9x + sin 3x))/((cos 7x + cos 5x) + (cos 9x + cos 3x)) = tan 6x`


Prove that: sin 3x + sin 2x – sin x = 4sin x `cos  x/2 cos  (3x)/2`


If \[\sin A = \frac{4}{5}\] and \[\cos B = \frac{5}{13}\], where 0 < A, \[B < \frac{\pi}{2}\], find the value of the following:
cos (A + B)


If \[\sin A = \frac{4}{5}\] and \[\cos B = \frac{5}{13}\], where 0 < A, \[B < \frac{\pi}{2}\], find the value of the following:
sin (A − B)


If \[\cos A = - \frac{24}{25}\text{ and }\cos B = \frac{3}{5}\], where π < A < \[\frac{3\pi}{2}\text{ and }\frac{3\pi}{2}\]< B < 2π, find the following:
cos (A + B)


Prove that

\[\frac{\cos 9^\circ + \sin 9^\circ}{\cos 9^\circ - \sin 9^\circ} = \tan 54^\circ\]

Prove that:
\[\cos^2 45^\circ - \sin^2 15^\circ = \frac{\sqrt{3}}{4}\]


Prove that:
sin2 B = sin2 A + sin2 (A − B) − 2 sin A cos B sin (A − B)


Prove that:
\[\tan\frac{\pi}{12} + \tan\frac{\pi}{6} + \tan\frac{\pi}{12}\tan\frac{\pi}{6} = 1\]


Prove that:
tan 36° + tan 9° + tan 36° tan 9° = 1


Prove that sin2 (n + 1) A − sin2 nA = sin (2n + 1) A sin A.

 

If sin (α + β) = 1 and sin (α − β) \[= \frac{1}{2}\], where 0 ≤ α, \[\beta \leq \frac{\pi}{2}\], then find the values of tan (α + 2β) and tan (2α + β).


If α + β − γ = π and sin2 α +sin2 β − sin2 γ = λ sin α sin β cos γ, then write the value of λ. 


If A + B + C = π, then \[\frac{\tan A + \tan B + \tan C}{\tan A \tan B \tan C}\] is equal to

 

If \[\cos P = \frac{1}{7}\text{ and }\cos Q = \frac{13}{14}\], where P and Q both are acute angles. Then, the value of P − Q is

 


If cot (α + β) = 0, sin (α + 2β) is equal to


\[\frac{\cos 10^\circ + \sin 10^\circ}{\cos 10^\circ - \sin 10^\circ} =\]

 


If \[\tan\theta = \frac{1}{2}\] and \[\tan\phi = \frac{1}{3}\], then the value of \[\tan\phi = \frac{1}{3}\] is 

 

 


If tan (A − B) = 1 and sec (A + B) = \[\frac{2}{\sqrt{3}}\], the smallest positive value of B is

 

If A − B = π/4, then (1 + tan A) (1 − tan B) is equal to 


Show that 2 sin2β + 4 cos (α + β) sin α sin β + cos 2(α + β) = cos 2α


If sinθ + cosecθ = 2, then sin2θ + cosec2θ is equal to ______.


3(sinx – cosx)4 + 6(sinx + cosx)2 + 4(sin6x + cos6x) = ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×