Advertisements
Advertisements
Question
The maximum distance of a point on the graph of the function y = `sqrt(3)` sinx + cosx from x-axis is ______.
Solution
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
APPEARS IN
RELATED QUESTIONS
Find the value of: sin 75°
Prove the following:
sin2 6x – sin2 4x = sin 2x sin 10x
Prove the following:
`(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x`
Prove the following:
cos 6x = 32 cos6 x – 48 cos4 x + 18 cos2 x – 1
If \[\sin A = \frac{3}{5}, \cos B = - \frac{12}{13}\], where A and B both lie in second quadrant, find the value of sin (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:
cos 47° cos 13° − sin 47° sin 13°
If \[\cos A = - \frac{12}{13}\text{ and }\cot B = \frac{24}{7}\], where A lies in the second quadrant and B in the third quadrant, find the values of the following:
sin (A + B)
If \[\cos A = - \frac{12}{13}\text{ and }\cot B = \frac{24}{7}\], where A lies in the second quadrant and B in the third quadrant, find the values of the following:
cos (A + B)
Prove that
\[\frac{\tan A + \tan B}{\tan A - \tan B} = \frac{\sin \left( A + B \right)}{\sin \left( A - B \right)}\]
Prove that \[\frac{\tan 69^\circ + \tan 66^\circ}{1 - \tan 69^\circ \tan 66^\circ} = - 1\].
Prove that:
tan 36° + tan 9° + tan 36° tan 9° = 1
If sin α sin β − cos α cos β + 1 = 0, prove that 1 + cot α tan β = 0.
Reduce each of the following expressions to the sine and cosine of a single expression:
cos x − sin x
Reduce each of the following expressions to the sine and cosine of a single expression:
24 cos x + 7 sin x
If 12 sin x − 9sin2 x attains its maximum value at x = α, then write the value of sin α.
Write the interval in which the value of 5 cos x + 3 cos \[\left( x + \frac{\pi}{3} \right) + 3\] lies.
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 tan \[\alpha = \frac{1}{1 + 2^{- x}}\] and \[\tan \beta = \frac{1}{1 + 2^{x + 1}}\] then write the value of α + β lying in the interval \[\left( 0, \frac{\pi}{2} \right)\]
If A + B + C = π, then sec A (cos B cos C − sin B sin C) is equal to
If A + B + C = π, then \[\frac{\tan A + \tan B + \tan C}{\tan A \tan B \tan C}\] is equal to
If \[\tan\alpha = \frac{x}{x + 1}\] and \[\tan\alpha = \frac{x}{x + 1}\], then \[\alpha + \beta\] is equal to
Express the following as the sum or difference of sines and cosines:
2 cos 3x sin 2xa
If f(x) = cos2x + sec2x, then ______.
[Hint: A.M ≥ G.M.]
If tanα = `1/7`, tanβ = `1/3`, then cos2α is equal to ______.
If sinx + cosx = a, then |sinx – cosx| = ______.
Given x > 0, the values of f(x) = `-3cos sqrt(3 + x + x^2)` lie in the interval ______.
State whether the statement is True or False? Also give justification.
If tanA = `(1 - cos B)/sinB`, then tan2A = tanB
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 |