Trigonometric Functions Online Objective Test | Trigonometric Functions Online Objective Test

# Trigonometric Functions # CBSE 11th Mathematics Prepare / Learn

Q1. In a triangle ABC, tan

\frac{A}{2} = \frac{5}{6}, \tan \frac{B}{2} = \frac{20}{37},

then tan

\frac{C}{2}

is equal to

A. 100222

B. 3437

C. 2/5

D. 5/2

Answer : Option C
Explaination / Solution:

# Trigonometric Functions # CBSE 11th Mathematics Prepare / Learn

Q2. In a triangle ABC, if A =

75^{o}

and B =

45^{o}

then b + 2 c is equal to

A. 12(a+b+c)

B. 2a

C. a+b+c

D. a

Answer : Option B
Explaination / Solution:

# Trigonometric Functions # CBSE 11th Mathematics Prepare / Learn

Q3. If the sides of a triangle are 13, 7, 8 the greatest angle of the triangle is

A. 3π2

B. π3

C. 2π3

D. π2

Answer : Option C
Explaination / Solution:

Let the sides of the triangle be a=13,b=7 and c=8.

Since a is the longest side the greatest angle is A.

Using Cosine rule, we have

$o s A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{49 + 64 - 169}{112} = \frac{- 1}{2} B u t w e h a v e c o s (\frac{2 π}{3}) = c o s (π - \frac{π}{3}) = - c o s (\frac{π}{3}) = \frac{- 1}{2} ∴ A = \frac{2 π}{3}$

# Trigonometric Functions # CBSE 11th Mathematics Prepare / Learn

Q4. There exists a triangle ABC satisfying the conditions

A. b sin A = a, a >> b

B. b sin A << a, a = b, A=π/2

C. bsinAπ/2

D. bsinA=a,A<π/2

Answer : Option D
Explaination / Solution:

$U s i n g s i n e r u l e w e h a v e \frac{a}{s i n A} = \frac{b}{s i n B} = k$

when k=1 we have

$b s i n A = a s i n B w h e n B = \frac{π}{2}, w e g e t b s i n A = a$

But we have in a triangle the sum of the three angles is 180 degrees ,so if B=90 degrees then $A < \frac{π}{2}$

# Trigonometric Functions # CBSE 11th Mathematics Prepare / Learn

Q5.

In a $Δ A B C,$ (b +c) cos A + (c + a) cos B + (a + b) cos C is equal to

A. 0

B. a+b+c

C. none of these

D. Rr

Answer : Option B
Explaination / Solution:

# Trigonometric Functions # CBSE 11th Mathematics Prepare / Learn

Q6. The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles. If the side b is 2, then the angle B is

A. 120∘

B. 90∘

C. 30∘

D. 60∘

Answer : Option B
Explaination / Solution:

$G i v e n a + b + c = \frac{6 (s i n A + s i n B + s i n C)}{3} \Rightarrow a + b + c = 2 (s i n A + s i n B + s i n C) N o w u s i n g s i n e r u l e a = k \sin A, b = k \sin B, c = k \sin C \Rightarrow k (s i n A + s i n B + s i n C) = 2 (s i n A + s i n B + s i n C) \Rightarrow k = 2$

Now when

# Trigonometric Functions # CBSE 11th Mathematics Prepare / Learn

Q7. In a triangle ABC,

\tan \frac{A + B}{2} \cot \frac{A - B}{2}

is equal to

A. none of these.

B. a−ba+b

C. a+ba-b

D. a−bc

Answer : Option C
Explaination / Solution:

$A + B + C = 180^{\circ} \Rightarrow \frac{C}{2} = 90^{\circ} - (\frac{A + B}{2})$

$∴ t a n (\frac{A - B}{2}) = \frac{a - b}{a + b} . c o t [90^{\circ} - (\frac{A + B}{2})] \Rightarrow t a n (\frac{A - B}{2}) = \frac{a - b}{a + b} . t a n (\frac{A + B}{2}) \Rightarrow t a n (\frac{A + B}{2}) . c o t (\frac{A - B}{2}) = \frac{a + b}{a - b}$

# Trigonometric Functions # CBSE 11th Mathematics Prepare / Learn

Q8. The area of a triangle is

80 c m^{2}

and its perimeter is 8 cm. The radius of its inscribed circle is

A. 20cm

B. 10cm

C. 5cm

D. none of these.

Answer : Option A
Explaination / Solution:

# Trigonometric Functions # CBSE 11th Mathematics Prepare / Learn

Q9. If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is

A. 4:5–√−1

B. (5–√−1):1

C. 5 : 1

D. 1:(5–√−1)

Answer : Option A
Explaination / Solution:

# Trigonometric Functions # CBSE 11th Mathematics Prepare / Learn

Q10. If a = 4, b = 3 and A =

60^{\circ}

then c is a root of the equation

A. x2−3x+7=0

B. x2−3x-7=0

x^{2} - 3 x + 7 = 0

x^{2} - 3 x + 7 = 0

D. x2−3x+7=0

Answer : Option B
Explaination / Solution:

$c o s A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} \Rightarrow c o s 60^{\circ} = \frac{1}{2} = \frac{9 + c^{2} - 16}{6 c} \Rightarrow c^{2} - 7 = 3 c \Rightarrow c^{2} - 3 c - 7 = 0$

Hence c is the root of the equation $x^{2} - 3 x - 7 = 0$

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