Trigonometry Test

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Trigonometry Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

The value of sin (45° + θ) – cos (45° – θ) is equal to

A
2 cosθ

B
0

C
2 sinθ

D
1
Question 2
1 / -0

If sinα = 1/2 and cosβ = 1/2, then the value of (α+β) is

A
0°

B
30°

C
60°

D
90°
Question 3
1 / -0

If sinθ – cosθ = 0, then what is the value of (sin⁴θ + cos⁴θ)? [Given (0º ≤ θ ≤ 90º)]

A
1

B
3/4

C
1/2

D
1/4
Question 4
1 / -0

The maximum value of sin x is

A
2

B
3

C
4

D
1
Question 5
1 / -0

The number of solutions of the equation 1 + sin x sin² x/2= 0 in [-π, π]is

A
0

B
1

C
2

D
3
Question 6
1 / -0

The area of a triangle is 80cm2 and its perimeter is 8 cm. The radius of its inscribed circle is

A
5 cm

B
20 cm

C
10 cm

D
none of these

Solution

We have if a,b,c are the sides of the triangle and r is the radius of the circle inscribed ,then

r=△/s, where 2s=a+b+c and△ denotes the area of the triangle.

Given △=80 and a+b+c=8

∴r=△/s=804=20cm
Question 7
1 / -0

tan x is periodic with period

A
π/2

B
π

C
2π

D
3π/2
Question 8
1 / -0

The magnitude of a radian is

A
180°

B
58°59′

C
57°17′44.8′′

D
60°
Question 9
1 / -0

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
60∘

B
90∘

C
30∘

D
120∘

Solution

Givena+b+c={(14.PNG)}

⇒a+b+c=2(sinA+sinB+sinC)

Now usings in erulea=ksinA,b=ksinB,c=ksinC⇒k(sinA+sinB+sinC)=2(sinA+sinB+sinC)⇒k=2

Now when b=2 we get

sinB=bk=22=1⇒B=90∘
Question 10
1 / -0

If tan A = 1/2 and tan B = 1/3, then the value of sin (A + B) is

A
1/2

B
1/√2

C
1/3

D
1/4

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Re-Attempt Weekly Quiz Competition

Trigonometry Test - 3

Result

Trigonometry Test - 3

Score

-

Rank

-

SHARING IS CARING

Question 1

2 cosθ

0

2 sinθ

1

Question 2

0°

30°

60°

90°

Question 3

1

3/4

1/2

1/4

Question 4

2

3

4

1

Question 5

0

1

2

3

Question 6

5 cm

20 cm

10 cm

none of these

Solution

Question 7

π/2

π

2π

3π/2

Question 8

180°

58°59′

57°17′44.8′′

60°

Question 9

60∘

90∘

30∘

120∘

Solution

Question 10

1/2

1/√2

1/3

1/4

User

Question Analysis

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Score

-

Rank

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