Visualisation of Trigonometric Ratios Using a Unit Circle

Q.

State whether the given statement is true or false:

$\cot$(90-$\theta$) = $\tan$ $\theta$

1. True

2. False

Q.

What is the value of 45 degrees if the value of 180 degrees is equal to pi?

1. pi/4

2. pi/2

3. pi

4. 3pi/4

Q.

$\frac{1}{1+ta{n}^2\theta }+\frac{1}{1+co{t}^2\theta }=$

1. -1

2. 0

3. 1

4. 2

Q. The trigonometric equations which hold true for any value of the angle are known as ____________ .

1. trignometric ratios
2. trignometric angles
3. trignometric identities
4. trignometric compliments

Q.

In triangle ABC, right angled at B, if $\angle$A is made larger and larger till it becomes ${90}^{\circ }$, what can you say about AC and AB if BC = 1 unit?

1. 0, 1

2. 1, 1

3. 1 , 0

4. 0, 0

Q.

Simplify :
4(1 – $si{n}^2\theta$) (1 + $ta{n}^2\theta$)

1. 4

2. 1

3. 2

4. 0

Q. For any value of $\theta$, $si{n}^2\theta +co{s}^2\theta =$ _______ .

1. $\frac{1}{2}$
2. 1
3. 0
4. 2

Q.

If $7si{n}^2\theta +3co{s}^2\theta =4$, then $sec\theta +cosec\theta$ is equal to

1. $\frac{2}{\sqrt{3}}-2$

2. $\frac{2}{\sqrt{3}}+2$

3. $\frac{2}{\sqrt{3}}$

4. None of these

Q.

If $sin\theta +si{n}^2\theta =1$, then find the value of $co{s}^4\theta +co{s}^2\theta -1$.

1. 2
2. 1
3. 0
4. -1

Q.

If
$cosec\theta -cot\theta =\frac{1}{2},0<\theta <{90}^{\circ }$,
then $cos\theta$
is equal to

1. $\frac{5}{3}$

2. $\frac{3}{5}$

3. $-\frac{3}{5}$

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