हिंदी

If tan θ = 3 and θ lies in third quadrant, then the value of sin θ ______.

Advertisements
Advertisements

प्रश्न

If tan θ = 3 and θ lies in third quadrant, then the value of sin θ  ______.

विकल्प

  • `1/sqrt(10)`

  • `- 1/sqrt(10)`

  • `(-3)/sqrt(10)`

  • `3/sqrt(10)`

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

If tanθ = 3 and θ lies in the third quadrant, then the value of sin θ `underline((-3)/sqrt(10))`.

Explanation:

tanθ = 3, θ lies in the third quadrant

∴ sinθ = `(-3)/sqrt(10)` where θ lies in third quadrant.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Trigonometric Functions - Exercise [पृष्ठ ५६]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
अध्याय 3 Trigonometric Functions
Exercise | Q 37 | पृष्ठ ५६

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Prove that  `2 sin^2  pi/6 + cosec^2  (7pi)/6 cos^2  pi/3 = 3/2`


Prove the following:

`(cos (pi + x) cos (-x))/(sin(pi - x) cos (pi/2 + x)) =  cot^2 x`


Prove the following:

`(cos9x - cos5x)/(sin17x - sin 3x) = - (sin2x)/(cos 10x)`


Prove the following:

`(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x`


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:
cos (A − B)


If \[\sin A = \frac{1}{2}, \cos B = \frac{\sqrt{3}}{2}\], where \[\frac{\pi}{2}\] < A < π and 0 < B < \[\frac{\pi}{2}\], find the following:
tan (A - B)


Evaluate the following:
sin 78° cos 18° − cos 78° sin 18°


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


If tan A + tan B = a and cot A + cot B = b, prove that cot (A + B) \[\frac{1}{a} - \frac{1}{b}\].


If tan x + \[\tan \left( x + \frac{\pi}{3} \right) + \tan \left( x + \frac{2\pi}{3} \right) = 3\], then prove that \[\frac{3 \tan x - \tan^3 x}{1 - 3 \tan^2 x} = 1\].


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 sin α sin β − cos α cos β + 1 = 0, prove that 1 + cot α tan β = 0.


If angle \[\theta\]  is divided into two parts such that the tangents of one part is \[\lambda\] times the tangent of other, and \[\phi\] is their difference, then show that\[\sin\theta = \frac{\lambda + 1}{\lambda - 1}\sin\phi\]

 

If \[\tan\theta = \frac{\sin\alpha - \cos\alpha}{\sin\alpha + \cos\alpha}\] , then show that \[\sin\alpha + \cos\alpha = \sqrt{2}\cos\theta\].


Find the maximum and minimum values of each of the following trigonometrical expression: 

12 cos x + 5 sin x + 4 


Reduce each of the following expressions to the sine and cosine of a single expression: 

\[\sqrt{3} \sin x - \cos x\] 


If x cos θ = y cos \[\left( \theta + \frac{2\pi}{3} \right) = z \cos \left( \theta + \frac{4\pi}{3} \right)\]then write the value of \[\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\] 


Write the maximum value of 12 sin x − 9 sin2 x. 


If a = b \[\cos \frac{2\pi}{3} = c \cos\frac{4\pi}{3}\] then write the value of ab + bc + ca.  


If sin α − sin β = a and cos α + cos β = b, then write the value of cos (α + β). 


If A + B + C = π, then sec A (cos B cos C − sin B sin C) is equal to


If 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =


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


If tan θ1 tan θ2 = k, then \[\frac{\cos \left( \theta_1 - \theta_2 \right)}{\cos \left( \theta_1 + \theta_2 \right)} =\]


The value of cos (36° − A) cos (36° + A) + cos (54° + A) cos (54° − A) is


The maximum value of \[\sin^2 \left( \frac{2\pi}{3} + x \right) + \sin^2 \left( \frac{2\pi}{3} - x \right)\] is


Express the following as the sum or difference of sines and cosines:

2 sin 3x cos x


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


If 3 tan (θ – 15°) = tan (θ + 15°), 0° < θ < 90°, then θ = ______.


Match each item given under column C1 to its correct answer given under column C2.

C1 C2
(a) `(1 - cosx)/sinx` (i) `cot^2  x/2`
(b) `(1 + cosx)/(1 - cosx)` (ii) `cot  x/2`
(c) `(1 + cosx)/sinx` (iii) `|cos x + sin x|`
(d) `sqrt(1 + sin 2x)` (iv) `tan  x/2`

If f(x) = cos2x + sec2x, then ______.

[Hint: A.M ≥ G.M.]


If α + β = `pi/4`, then the value of (1 + tan α)(1 + tan β) is ______.


If tanα = `1/7`, tanβ = `1/3`, then cos2α is equal to ______.


If sinx + cosx = a, then sin6x + cos6x = ______.


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


State whether the statement is True or False? Also give justification.

If tan(π cosθ) = cot(π sinθ), then `cos(theta - pi/4) = +- 1/(2sqrt(2))`.


In the following match each item given under the column C1 to its correct answer given under the column C2:

Column A Column B
(a) sin(x + y) sin(x – y) (i) cos2x – sin2y
(b) cos (x + y) cos (x – y) (ii) `(1 - tan theta)/(1 + tan theta)`
(c) `cot(pi/4 + theta)` (iii) `(1 + tan theta)/(1 - tan theta)`
(d) `tan(pi/4 + theta)` (iv) sin2x – sin2y

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×