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The maximum value of $\sin (x + \frac{π}{6}) + \cos (x + \frac{π}{6})$ in the interval $(0, \frac{π}{2})$ is attained at

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Important Questions on Trigonometric Ratios and Identities

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Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

In a triangle

P Q R, A, B

and

C

are the angles opposite to the corresponding sides of lengths

a, b

and

c

, respectively. If the sides are

a = 5, b = 13

and

c = 12

, then

\sin \frac{B}{2} + \cos \frac{B}{2} =

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Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

The value of

\frac{\tan 330 ° \sec 420 ° \sin 300 °}{\tan 135 ° \sin 210 ° \sec 315 °}

is equal to

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Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

f (x) = \sqrt{[(\sin 2 x + 2) (\cos 2 x + 2)]}

for

x

is a real number, then which of the following values lies in the domain of

f (x)

but NOT in the range of

f (x) ?

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

The value of

\cos 1200 ° + \tan 1485 °

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

\tan 1 ° \times \tan 2 ° \times \tan 3 ° \times \dots \dots \dots \dots \times \tan 89 ° =

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

cosec 39 ° = q,

then the value of

\frac{1}{{cosec}^{2} 51^{°}} + \sin^{2} 39^{°} + \tan^{2} 51^{°} - \frac{1}{\sin^{2} 51^{°} \sec^{2} 39^{°}} + 1

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

The number of solutions of the equation

|\cot x| = \cot x + \frac{1}{\sin x}, 0 \leq x \leq 2 π

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

Let

θ

be an angle in the standard position such that the point

(- 5, 12)

lies on its terminal side, then

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

\sec θ = \frac{13}{12}, θ

lies in

4^{th}

quadrant, then

\tan θ \times cosec θ \times \sin θ \times \cos θ =

HARD

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

A = \{x \in [0, 2 π] / \tan x - \tan^{2} x > 0\}

and

B = \{x \in [0, 2 π] / | \sin x | < \frac{1}{2}\},

then

A \cap B =

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Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

The value of

\tan 1 ° \tan 2 ° \tan 3 ° \dots \tan 89 °

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Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

\cos (θ_{1}) + \cos (θ_{2}) + \cos (θ_{3}) + \cos (θ_{4}) = - 4,

then the value of

\cot (\frac{θ_{1}}{2}) + \cot (\frac{θ_{2}}{2}) + \cot (\frac{θ_{3}}{2}) + \cot (\frac{θ_{4}}{2}) =

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

The range of the function

f (x) = \log_{\sqrt{5}} (3 + \cos (\frac{3 π}{4} + x) + \cos (\frac{π}{4} + x) + \cos (\frac{π}{4} - x) - \cos (\frac{3 π}{4} - x))

is :

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

W, X, Y

and

Z

are four angles taken in order of a cyclic quadrilateral, then the value of

(13 + \cot W + \cot X + \cot Y + \cot Z + 13)

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Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

The value of

2 \sin (\frac{π}{8}) \sin (\frac{2 π}{8}) \sin (\frac{3 π}{8}) \sin (\frac{5 π}{8}) \sin (\frac{6 π}{8}) \sin (\frac{7 π}{8})

is :

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

The number of solutions of the equation

\sin x = \cos^{2} x

in the interval

(0, 10)

is ______.

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

The trigonometric function

y = \tan x

in the

II

quadrant

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

The graphs of the polynomial

x^{2} - 1

and

\cos x

intersect

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

The value of

\sin^{2} 51 ° + \sin^{2} 39 °

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Range of Trigonometric Expressions

The angle of elevation of the top of a vertical tower from a point A, due east of it is

45^{o}

. The angle of elevation of the top of the same tower from a point B, due south of A is

30^{o}

. If the distance between A and B is

54 \sqrt{2} m

, then the height of the tower (in meters), is:

The maximum value of sin⁡x+π6+cos⁡x+π6 in the interval 0,π2 is attained at

Important Questions on Trigonometric Ratios and Identities

Learn and Prepare for any exam you want !

The maximum value of $\sin (x + \frac{π}{6}) + \cos (x + \frac{π}{6})$ in the interval $(0, \frac{π}{2})$ is attained at