Variation of Trigonometric Ratios from 0 to 90 Degrees

Q.

How do you find the exact value of $\sin {105}^0$.

Q.

Evaluate:$\cos 60°\times \cos 30°+\sin 60°\times \sin 30°$

Q.

Find the value of the trigonometric function $\sin 765°$.

Q.

The values of both sine and cosine of an angle increase from 0 to 1, where the angle varies from $0^{\circ }\text{to}{90}^{\circ }$.

1. True

2. False

Q. Question 2
Write ‘True’ or ‘False’ and justify your answer in each of the following:
The value of the expression $(co{s}^2{23}^{\circ }-si{n}^2{67}^{\circ })$ is positive.

Q. Question 10
If $sin\alpha =\frac{1}{2}$ and $cos\beta =\frac{1}{2}$, then the value of $(\alpha +\beta )$ is

(A) $0^{\circ }$
(B) ${30}^{\circ }$
(C) ${60}^{\circ }$
(D) ${90}^{\circ }$

Q.

The values of cosecant of an angle ___ , when the angle varies from $0^{\circ }\text{to}{90}^{\circ }$.

Q. Question 5
If $sec4A=cosec(A-{20}^{\circ })$, where 4A is an acute angle, find the value of A.

Q. Question 11 (iii)
State whether the following are true or false. Justify your answer.
(iii) cos A is the abbreviation used for the cosecant of angle A.

Q. Question 4 (iii)
State whether the following are true or false. Justify your answer.
(iii) The value of cos $\theta$ increases as $\theta$ increases.

Q. Question 2 (i)
Show that :
$tan{48}^{\circ }tan{23}^{\circ }tan{42}^{\circ }tan{67}^{\circ }=1$

Q. The cosecant of an angle equals the ____ of its complement.

1. secant
2. tangent
3. sine
4. cosine

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. 1, 1

2. 1 , 0

3. 0, 1

4. 0, 0

Q. If $tan\theta$ = 2, then $cot\theta$ = $\frac{1}{2}$

1. False
2. True

Q. Evaluate:$\cos {225}^{\circ }-\sin {225}^{\circ }$

Q. $tan{1}^{\circ }.tan{2}^{\circ }.tan{3}^{\circ }...tan{89}^{\circ }$=_________.

1. 0
2. 1
3. $tan{90}^{\circ }$
4. $\sqrt{3}$

Q. If $\sin \theta =\alpha$ then, $\tan \theta$=......... .

1. $\alpha$
2. $\frac{\alpha }{1-{\alpha }^2}$
3. $\sqrt{1-{\alpha }^2}$
4. $\frac{\alpha }{\sqrt{1-{\alpha }^2}}$

Q.

In $\Delta$ABC, right angled at B, if $\angle A$ is made smaller and smaller till it becomes zero, find the value of sin A and cos A.

1. 0, 1

2. 0, Not defined

3. Not defined, 0

4. 0, $\sqrt{3}$

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. In $△$ABC, if $\angle B={90}^{\circ },tanA=\frac{1}{\sqrt{3}}$, then $sinAcosC+cosAsinC$=

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

Q. Show that $\frac{co{s}^2({45}^{\circ }+\theta )+co{s}^2({45}^{\circ }-\theta )}{tan({60}^{\circ }+\theta )tan({30}^{\circ }-\theta )}=1$

Q. $\sin {20}^{\circ }\sin {40}^{\circ }\sin {60}^{\circ }\sin {80}^{\circ }=\frac{k}{16}$. Find the value of $k$.

Q. Prove that :
$ta{n}^2\theta -\frac{1}{co{s}^2\theta }=-1$

Q. Question 4 (iii)
State whether the following are true or false. Justify your answer.
(iii) The value of cos $\theta$ increases as $\theta$ increases.

Q. Which of the following statements is/are true for $\theta$ ranging from $0^{\circ }$ to ${90}^{\circ }$?

1. $sin\theta ,tan\theta andsec\theta$ increases as $\theta$ increases
2. $sin\theta =cos\theta$ for all the values of $\theta$
3. $cos\theta ,cot\theta andcosec\theta$ increases as $\theta$ increases
4. Trigonometric ratios values do not follow any pattern

Q. Show that $\frac{co{s}^2({45}^{\circ }+\theta )+co{s}^2({45}^{\circ }-\theta )}{tan({60}^{\circ }+\theta )tan({30}^{\circ }-\theta )}=1$

Q. The ratio of sec$\theta$ can also be represented as $\frac{1}{sin\theta }$.

1. True
2. False

Q.

In the case of tangent of an angle, the values increase from 0 to infinity, when the angle increases from $0^{\circ }\text{to}{90}^{\circ }$.

1. True

2. False

Q.

$\frac{\text{sin}\theta \text{cos}({90}^{\circ }-\theta )\text{cos}\theta }{\text{sin}({90}^{\circ }-\theta )}+\frac{\text{cos}\theta \text{sin}({90}^{\circ }-\theta )\text{sin}\theta }{\text{cos}({90}^{\circ }-\theta )}=$ ___

1. - 1

2. 0

3. 1

4. 2

Q. The ratio of sec$\theta$ can also be represented as $\frac{1}{sin\theta }$.

1. True
2. False