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Trigonometry - Mathematics Questions asked by Filo students

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tan^{2} θ = 1 - e^{2}

sec θ + tan^{3} θ cosec θ = (2 - e^{2})^{3/2}

{"3. Prove the following:","(i) $co s^{2} t h e t a + co s^{2} l e f t (t h e t a + 12 0^{c i rc} r i g h t) + co s^{2} l e f t (t h e t a - 12 0^{c i rc} r i g h t) = 3/2$ .","(ii) $(sec A - o p er a t or nam e cosec A) (1 + t an A + co t A) = t an A sec A - co t A o p er a t or nam e cosec A$ .","(iii) $(o p er a t or nam e cosec t h e t a - sec t h e t a) (co t t h e t a - t an t h e t a) = (o p er a t or nam e cosec t h e t a + sec t h e t a) (sec t h e t a o p er a t or nam e cosec t h e t a - 2)$ "}

Topic:

Trigonometry

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Views: 5,843

TRIGONOMETRIC RATIOS : DEFINITION, SIGNS PERIODS THEIR GRAPHS AND THEIR FUNDAMENTAL RELATIONS 1. If

f (x) = cos x - sin x

f (1)

positive
negative
does not exist
none of these

Topic:

Trigonometry

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Views: 6,103

Q.4 Express the following angles in degree, minute and second. i)

(183.7)^{\circ}

(245.33)^{0}

(\frac{1}{5})^{c}

Topic:

Trigonometry

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Views: 5,689

(ii) Find the average of

sin 2^{\circ}, sin 4^{\circ}, sin 6^{\circ}, \dots\dots, sin 18 0^{\circ}

(iii) Prove that

cos \frac{π}{11} + cos \frac{3 π}{11} + cos \frac{5 π}{11} + cos \frac{7 π}{11} + cos \frac{9 π}{11} = \frac{1}{2}

\frac{c o t 1 ^{0}}{90}

[2] Find sum of the following series: (14)

cos \frac{π}{2 n + 1} + cos \frac{3 π}{2 n + 1} + cos \frac{5 π}{2 n + 1} + \dots\dots

n

sin 2 α + sin 3 α + sin 4 α + \dots .. + sin n α

(n + 2) α = 2 π

Topic:

Trigonometry

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Views: 5,364

Draw the angles of the following measures and determine their quadrants.

$- 14 0^{\circ}$
$25 0^{\circ}$ iii) $42 0^{\circ}$
$75 0^{\circ}$
$94 5^{\circ}$ vi) $112 0^{\circ}$ vii) $- 8 0^{\circ}$ viii) $- 33 0^{\circ}$

Topic:

Trigonometry

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Views: 5,875

3 tan α tan β = 1

2 cos (α + β) = cos (α - β)

8. Eliminate $θ$ if $tan (θ - α) = a$ and $tan (θ + α) = b$ .
9. Prove that:
(ii) $tan A + tan (6 0^{\circ} + A) + tan (12 0^{\circ} + A) = 3 tan 3 A$
(iii) $\frac{t a n 6 9 ^{\circ} + t a n 6 6 ^{\circ}}{1 - t a n 6 9 ^{\circ} t a n 6 6 ^{\circ}} = - 1$

Topic:

Trigonometry

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Views: 5,985

The number of solutions of the equation lying in the interval are

0
1
2
3

Topic:

Trigonometry & Logarithm

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Views: 5,145

Prove that Cos 15° + sin 15° / cos 15° - sin 15° = √3

Topic:

Trigonometry

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Views: 5,900

tan^{2} θ = 2 tan^{2} ϕ + 1

, then the value of

cos 2 θ + sin^{2} ϕ

1
2
$- 1$
Independent of $ϕ$

Topic:

Trigonometry

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Question 10

Views: 5,674

C-1. The value of

\frac{1 - t a n ^{2} 1 5 ^{\circ}}{1 + t a n ^{2} 1 5 ^{\circ}}

1
$3$
$\frac{3}{2}$
2

Topic:

Trigonometry

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Question 11

Views: 5,489

n second quadrant. nometric functions in Exercises 6 to

10.

cosec (- 141 0^{\circ})

Topic:

Trigonometry

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Question 12

Views: 5,794

The variation of

y = \frac{1}{x}

is best shown by

$3 0^{\circ}$
$6 0^{\circ}$ ::
$9 0^{\circ}$

Topic:

Trigonometry

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Question 13

Views: 5,319

cos (\frac{x}{2})

is equal to (If

tan x = \frac{5}{12}

x

lies in III quadrant)

$\frac{5}{13}$
$\frac{5}{26}$
$\frac{5}{13}$
$- \frac{1}{26}$

Topic:

Trigonometry

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Question 14

Views: 5,858

1) Describe the following sets in Roster form i)

A = {x / x

isaletteroftheword

^{'} MO V EMEN T^{'}}

B = {x / x

- \frac{3}{2} < x < \frac{9}{2}}

C = {x / x = 2 n + 1, n \in N}

Topic:

Trigonometry

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Question 15

Views: 5,509

\sum_{k = 1}^{35} sin 5 k^{\circ} = tan (\frac{m}{n})^{\circ}

m

n

are relatively prime positive integers that satisfy

(\frac{m}{n})^{\circ} < 9 0^{\circ}

m + n

173
175
177
179

Topic:

Trigonometry

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Question 16

Views: 5,690

How many degrees are oovered by hour hand and minute hand in one hour?

Topic:

Trigonometry

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Question 17

Views: 5,633

In Fig. 5.47, the value of

cos ϕ

$\frac{5}{4}$
$\frac{5}{3}$
$\frac{3}{5}$
$\frac{4}{5}$

Topic:

Trigonometry

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Question 18

Views: 5,993

= \frac{2}{s i n \frac{α + γ}{2}} = \frac{2}{2 s i n \frac{α + γ}{2} s i n \frac{α - γ}{2}} = \frac{s i n α - s i n γ}{c o s γ - c o s α}

IIlustration 4: Show that

sin 1 2^{\circ} . sin 4 8^{\circ} \cdot sin 5 4^{\circ} = 1/8

Topic:

Trigonometry

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Question 19

Views: 5,716

= - cos (\frac{A + B}{2}) + sin \frac{B}{2} + sin \frac{A}{2} = - sin \frac{C}{2} + sin \frac{B}{2} + sin \frac{A}{2} = L.H.S.

A, B, C

are angles in a triangle, then prove that

sin 2 A - sin 2 B + sin 2 C = 4 cos A sin B cos C

Topic:

Trigonometry

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Question 20

Views: 5,832

α

β

are the roots of the equation

x^{2} + 6 x + λ = 0

3 α + 2 β = - 20

λ =

$- 8$
$- 16$
16
8

Topic:

Trigonometry

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