Introduction to Trigonometry Test

Result

Introduction to Trigonometry Test - 22

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$\tan 0^{\circ}$$ is

A
$$0$$

B
$$\dfrac {1}{2}$$

C
$$\dfrac {\sqrt {3}}{2}$$

D
$$1$$

Solution

$$\tan\ 0^o=\dfrac{\sin\ 0^o}{\cos\ 0^o}\\=\dfrac01\\=0$$
Question 2
1 / -0

The value of $$\sin 0^{\circ}$$ is _______.

A
$$0$$

B
$$\dfrac {1}{2}$$

C
$$\dfrac {\sqrt {3}}{2}$$

D
$$1$$

Solution

Using the trigonometric table,
The value of $$\sin 0^o$$ is $$0$$.
Question 3
1 / -0

For an acute angle $$\theta$$ in a right angled triangle, $$\tan{\theta} =$$

A
$$\dfrac{1}{\cot{\theta}}$$

B
$$\dfrac{1}{\sec{\theta}}$$

C
$$\dfrac{1}{\text{cosec}\,{\theta}}$$

D
None of these

Solution

$$\tan{\theta} = \dfrac{\text{perpendicular}}{\text{base}}$$ and
$$\dfrac{1}{\cot{\theta}} = \dfrac{1}{\dfrac{\text{base}}{\text{perpendicular}}} = \dfrac{\text{perpendicular}}{\text{base}}$$.
Hence, $$\tan{\theta} = \dfrac{1}{\cot{\theta}}$$.
Question 4
1 / -0

Evaluate: $$\text{cosec }0^{\circ} $$

A
$$0$$

B
$$\dfrac {1}{2}$$

C
$$1$$

D
Undefined

Solution

Using trigonometric ratio value of $$\csc { { 0^o } } =Undefined$$
As,$$\csc { { 0^o } } =\dfrac { 1 }{ \sin { { 0^o } } } =\dfrac { 1 }{ 0 } =undefined$$
Question 5
1 / -0

The value of $$\sec 90^{\circ}$$ is

A
$$1$$

B
$$\dfrac {2}{\sqrt {3}}$$

C
$$\sqrt {2}$$

D
None of these

Solution

$$\sec 90° = \dfrac{1}{\cos 90°}=\dfrac{1}{0},$$ undefined.

Hence, the answer is none of these.
Question 6
1 / -0

The value of $$\cos 90^{\circ}$$ is ______.

A
$$0$$

B
$$1$$

C
$$\dfrac {1}{2}$$

D
$$\dfrac {\sqrt {3}}{2}$$

Solution

Using the trigonometric table $$\cos 90^0$$ is $$ 0$$
Question 7
1 / -0

The inverse of $$\tan\theta$$ is

A
$${\cot\theta}$$

B
$${\tan\theta}$$

C
$${\cos\theta}$$

D
$${\sin\theta}$$

Solution

We know $$\tan\theta = \dfrac PB$$
So, inverse of $$\tan\theta$$ $$=\dfrac BP$$ $$=\cot\theta$$
Question 8
1 / -0

Find the value of $$\tan\theta . \cot\theta$$.

A
$$2$$

B
$$1$$

C
$$3$$

D
$$4$$

Solution

$$\tan\theta = \dfrac{1}{\cot\theta}$$
Therefore,
$$\tan\theta . \cot\theta =\tan\theta . \dfrac{1}{\tan \theta} = 1$$
Question 9
1 / -0

The value of $$\sin 90^{\circ}$$ is _____

A
$$0$$

B
$$1$$

C
$$\dfrac {1}{2}$$

D
$$\dfrac {\sqrt {3}}{2}$$

Solution

$$\sin90^o=1$$
Question 10
1 / -0

The value of $$\cot 0^{\circ}$$ is _____

A
$$0$$

B
$$1$$

C
$$\dfrac {1}{2}$$

D
Not defined

Solution

Using trigonometric ratio
$$\cot { { 0^o } } =\dfrac { 1 }{ \tan { { 0^o } } } \\=\dfrac { 1 }{ 0 }$$

But $$\dfrac{1}{0}$$ is not defined, hence $$cot\ 0^o$$ is not defined

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Re-Attempt Weekly Quiz Competition

Introduction to Trigonometry Test - 22

Result

Introduction to Trigonometry Test - 22

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SHARING IS CARING

Question 1

$$0$$

$$\dfrac {1}{2}$$

$$\dfrac {\sqrt {3}}{2}$$

$$1$$

Solution

Question 2

$$0$$

$$\dfrac {1}{2}$$

$$\dfrac {\sqrt {3}}{2}$$

$$1$$

Solution

Question 3

$$\dfrac{1}{\cot{\theta}}$$

$$\dfrac{1}{\sec{\theta}}$$

$$\dfrac{1}{\text{cosec}\,{\theta}}$$

None of these

Solution

Question 4

$$0$$

$$\dfrac {1}{2}$$

$$1$$

Undefined

Solution

Question 5

$$1$$

$$\dfrac {2}{\sqrt {3}}$$

$$\sqrt {2}$$

None of these

Solution

Question 6

$$0$$

$$1$$

$$\dfrac {1}{2}$$

$$\dfrac {\sqrt {3}}{2}$$

Solution

Question 7

$${\cot\theta}$$

$${\tan\theta}$$

$${\cos\theta}$$

$${\sin\theta}$$

Solution

Question 8

$$2$$

$$1$$

$$3$$

$$4$$

Solution

Question 9

$$0$$

$$1$$

$$\dfrac {1}{2}$$

$$\dfrac {\sqrt {3}}{2}$$

Solution

Question 10

$$0$$

$$1$$

$$\dfrac {1}{2}$$

Not defined

Solution

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