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First Year Math Fundamentals of Trigonometry 2. Convert the following into degree measure:(v) \frac{3}{2} radians


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2. Convert the following into degree measure:(v) \frac{3}{2} radians

Q.43 1-\sec ^{2} \theta= is equal to(a) \tan ^{2} \theta (b) -\tan ^{2} \theta (c) \tan ^{2} \theta-1 (d) 1-\tan ^{2} \theta
Q.43  1-\sec ^{2} \theta=  is equal to(a)  \tan ^{2} \theta (b)  -\tan ^{2} \theta (c)  \tan ^{2} \theta-1 (d)  1-\tan ^{2} \theta

Q.43 1-\sec ^{2} \theta= is equal to(a) \tan ^{2} \theta (b) -\tan ^{2} \theta (c) \tan ^{2} \theta-1 (d) 1-\tan ^{2} \theta

1. Verify the following:(iii) 2 \sin 45^{\circ}+\frac{1}{2} \operatorname{cosec} 45^{\circ}=\frac{3}{\sqrt{2}}
1. Verify the following:(iii)  2 \sin 45^{\circ}+\frac{1}{2} \operatorname{cosec} 45^{\circ}=\frac{3}{\sqrt{2}}

1. Verify the following:(iii) 2 \sin 45^{\circ}+\frac{1}{2} \operatorname{cosec} 45^{\circ}=\frac{3}{\sqrt{2}}

2. Evaluate the following:ii) \frac{1-\tan ^{2} \frac{\pi}{3}}{1+\tan ^{2} \frac{\pi}{3}}
2. Evaluate the following:ii)  \frac{1-\tan ^{2} \frac{\pi}{3}}{1+\tan ^{2} \frac{\pi}{3}}

2. Evaluate the following:ii) \frac{1-\tan ^{2} \frac{\pi}{3}}{1+\tan ^{2} \frac{\pi}{3}}

Q.21 80^{\circ}= (a) \frac{5 \pi}{6} radians (b) \frac{4 \pi}{9} radians (c) \frac{\pi}{4} radians(d) 180 \pi radians
Q.21  80^{\circ}= (a)  \frac{5 \pi}{6}  radians (b)  \frac{4 \pi}{9}  radians (c)  \frac{\pi}{4}  radians(d)  180 \pi  radians

Q.21 80^{\circ}= (a) \frac{5 \pi}{6} radians (b) \frac{4 \pi}{9} radians (c) \frac{\pi}{4} radians(d) 180 \pi radians

Evaluate:1. \sin \frac{\pi}{3} \cos \frac{\pi}{6}-\cos \frac{\pi}{3} \sin \frac{\pi}{6}
Evaluate:1.  \sin \frac{\pi}{3} \cos \frac{\pi}{6}-\cos \frac{\pi}{3} \sin \frac{\pi}{6}

Evaluate:1. \sin \frac{\pi}{3} \cos \frac{\pi}{6}-\cos \frac{\pi}{3} \sin \frac{\pi}{6}

1. Find the signs of the following trigonometric functions.(v) \tan 299^{\circ}
1. Find the signs of the following trigonometric functions.(v)  \tan 299^{\circ}

1. Find the signs of the following trigonometric functions.(v) \tan 299^{\circ}

7. If \tan \theta=\frac{1}{\sqrt{7}} and the terminal arm of the angle is not in the III . find the values of \frac{\csc ^{2} \theta-\sec ^{2} \theta}{\csc ^{2} \theta+\sec ^{2} \theta}
7. If  \tan \theta=\frac{1}{\sqrt{7}}  and the terminal arm of the angle is not in the III . find the values of  \frac{\csc ^{2} \theta-\sec ^{2} \theta}{\csc ^{2} \theta+\sec ^{2} \theta}

7. If \tan \theta=\frac{1}{\sqrt{7}} and the terminal arm of the angle is not in the III . find the values of \frac{\csc ^{2} \theta-\sec ^{2} \theta}{\csc ^{2} \theta+\sec ^{2} \theta}

7. find the arc length of a unit circle corresponding to the central angle measuring:(ii) 60^{\circ}
7. find the arc length of a unit circle corresponding to the central angle measuring:(ii)  60^{\circ}

7. find the arc length of a unit circle corresponding to the central angle measuring:(ii) 60^{\circ}

19. \frac{1}{\operatorname{cosec} \theta-\cot \theta}-\frac{1}{\sin \theta}=\frac{1}{\sin \theta}-\frac{1}{\operatorname{cosec} \theta+\cot \theta}
19.  \frac{1}{\operatorname{cosec} \theta-\cot \theta}-\frac{1}{\sin \theta}=\frac{1}{\sin \theta}-\frac{1}{\operatorname{cosec} \theta+\cot \theta}

19. \frac{1}{\operatorname{cosec} \theta-\cot \theta}-\frac{1}{\sin \theta}=\frac{1}{\sin \theta}-\frac{1}{\operatorname{cosec} \theta+\cot \theta}

1. Express the following sexagesimal measures of angles in radians:(ix) 150^{\circ}
1. Express the following sexagesimal measures of angles in radians:(ix)  150^{\circ}

1. Express the following sexagesimal measures of angles in radians:(ix) 150^{\circ}

1. Find the signs of the following trigonometric functions.(x) \sin \frac{3}{4} \pi
1. Find the signs of the following trigonometric functions.(x)  \sin \frac{3}{4} \pi

1. Find the signs of the following trigonometric functions.(x) \sin \frac{3}{4} \pi

Prove the following identities state the domain of \theta in each case:24. \frac{\cos \theta+\sin \theta}{\cos \theta-\sin \theta}+\frac{\cos \theta-\sin \theta}{\cos \theta+\sin \theta}=\frac{2}{1-2 \sin ^{2} \theta}
Prove the following identities state the domain of  \theta  in each case:24.  \frac{\cos \theta+\sin \theta}{\cos \theta-\sin \theta}+\frac{\cos \theta-\sin \theta}{\cos \theta+\sin \theta}=\frac{2}{1-2 \sin ^{2} \theta}

Prove the following identities state the domain of \theta in each case:24. \frac{\cos \theta+\sin \theta}{\cos \theta-\sin \theta}+\frac{\cos \theta-\sin \theta}{\cos \theta+\sin \theta}=\frac{2}{1-2 \sin ^{2} \theta}

2. Convert the following into degree measure :(1) \frac{2}{3} \pi radians
2. Convert the following into degree measure :(1)  \frac{2}{3} \pi  radians

2. Convert the following into degree measure :(1) \frac{2}{3} \pi radians

14. Show that the area of a sector of a circular region of radius r is \frac{1}{2} r^{2} \theta where \theta is the circular measure of the central angle of the sector.
14. Show that the area of a sector of a circular region of radius  r  is  \frac{1}{2} r^{2} \theta  where  \theta  is the circular measure of the central angle of the sector.

14. Show that the area of a sector of a circular region of radius r is \frac{1}{2} r^{2} \theta where \theta is the circular measure of the central angle of the sector.

4. Find the values of the remaining trigonometric functions:v) \sin \theta=-\frac{1}{\sqrt{2}} and the terminal arm of the angle is not in . III.
4. Find the values of the remaining trigonometric functions:v)  \sin \theta=-\frac{1}{\sqrt{2}}  and the terminal arm of the angle is not in . III.

4. Find the values of the remaining trigonometric functions:v) \sin \theta=-\frac{1}{\sqrt{2}} and the terminal arm of the angle is not in . III.

(n) 3 radians is equal in degrees:(a) 169.78^{\circ} (b) 171.888^{\circ} (c) 170.889^{\circ} (d) 171.5^{\circ}
(n) 3 radians is equal in degrees:(a)  169.78^{\circ} (b)  171.888^{\circ} (c)  170.889^{\circ} (d)  171.5^{\circ}

(n) 3 radians is equal in degrees:(a) 169.78^{\circ} (b) 171.888^{\circ} (c) 170.889^{\circ} (d) 171.5^{\circ}

1. Convert the following into radian measure :\[\text { (0) } 45^{\circ}\]
1. Convert the following into radian measure :\[\text { (0) } 45^{\circ}\]

1. Convert the following into radian measure :\[\text { (0) } 45^{\circ}\]

Find the remaining trigonometric functions in the following if6. \operatorname{cosec} 8=-\frac{3}{2} and \rho (B) is not in the fourth rant.
Find the remaining trigonometric functions in the following if6.  \operatorname{cosec} 8=-\frac{3}{2}  and  \rho  (B) is not in the fourth rant.

Find the remaining trigonometric functions in the following if6. \operatorname{cosec} 8=-\frac{3}{2} and \rho (B) is not in the fourth rant.

2. Convert the following radian measures of angles into the measures of sexagesimal system:iv) \frac{\pi}{3}
2. Convert the following radian measures of angles into the measures of sexagesimal system:iv)  \frac{\pi}{3}
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2. Convert the following radian measures of angles into the measures of sexagesimal system:iv) \frac{\pi}{3}

1. Convert the following into radian measure (v) -70^{\circ} 9^{\circ}
1. Convert the following into radian measure (v)  -70^{\circ} 9^{\circ}
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1. Convert the following into radian measure (v) -70^{\circ} 9^{\circ}

1. Find the signs of the following:iii) \tan 115^{\circ}
1. Find the signs of the following:iii)  \tan 115^{\circ}
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1. Find the signs of the following:iii) \tan 115^{\circ}

Prove the following identities state the domain of \theta in each case:10. \frac{\cos \theta-\sin \theta}{\cos \theta+\sin \theta}=\frac{\cot \theta-1}{\cot \theta+1}
Prove the following identities state the domain of  \theta  in each case:10.  \frac{\cos \theta-\sin \theta}{\cos \theta+\sin \theta}=\frac{\cot \theta-1}{\cot \theta+1}
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Prove the following identities state the domain of \theta in each case:10. \frac{\cos \theta-\sin \theta}{\cos \theta+\sin \theta}=\frac{\cot \theta-1}{\cot \theta+1}

10. A horse is tethered to a peg by a rope of 9 meters length and it can move in a circle with the peg as centre. If the horse moves along the circumference of the circle keeping the rope tight how far will it have gone when the rope has turned through an angle of 70^{\circ} ?
10. A horse is tethered to a peg by a rope of 9 meters length and it can move in a circle with the peg as centre. If the horse moves along the circumference of the circle keeping the rope tight how far will it have gone when the rope has turned through an angle of  70^{\circ}  ?
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10. A horse is tethered to a peg by a rope of 9 meters length and it can move in a circle with the peg as centre. If the horse moves along the circumference of the circle keeping the rope tight how far will it have gone when the rope has turned through an angle of 70^{\circ} ?

2. Fill in the blanks:i) \sin \left(-310^{\circ}\right)=\ldots . \sin 310^{\circ}
2. Fill in the blanks:i)  \sin \left(-310^{\circ}\right)=\ldots . \sin 310^{\circ}
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2. Fill in the blanks:i) \sin \left(-310^{\circ}\right)=\ldots . \sin 310^{\circ}

2. Convert the following into degree measure:(v) \frac{3}{2} radians
2. Convert the following into degree measure:(v)  \frac{3}{2}  radians
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2. Convert the following into degree measure:(v) \frac{3}{2} radians

Evaluate:2. \sin \frac{\pi}{4} \cos \frac{\pi}{4}-\tan \frac{\pi}{4}
Evaluate:2.  \sin \frac{\pi}{4} \cos \frac{\pi}{4}-\tan \frac{\pi}{4}
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Evaluate:2. \sin \frac{\pi}{4} \cos \frac{\pi}{4}-\tan \frac{\pi}{4}

3. Find B i f s=20 \mathrm{~cm} and r \approx 5 \mathrm{~cm} .
3. Find  B i f s=20 \mathrm{~cm}  and  r \approx 5 \mathrm{~cm} .
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3. Find B i f s=20 \mathrm{~cm} and r \approx 5 \mathrm{~cm} .

13. A circular wire of radius 6 \mathrm{~cm} is cut straightened and then bent so as to lie along the circumference of a hoop of radius 24 \mathrm{~cm} . Find the measure of the angle which it subtends at the centre of the hoop.
13. A circular wire of radius  6 \mathrm{~cm}  is cut straightened and then bent so as to lie along the circumference of a hoop of radius  24 \mathrm{~cm} . Find the measure of the angle which it subtends at the centre of the hoop.
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13. A circular wire of radius 6 \mathrm{~cm} is cut straightened and then bent so as to lie along the circumference of a hoop of radius 24 \mathrm{~cm} . Find the measure of the angle which it subtends at the centre of the hoop.

7. find the arc length of a unit circle corresponding to the central angle measuring:(i) 30^{\circ}
7. find the arc length of a unit circle corresponding to the central angle measuring:(i)  30^{\circ}
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7. find the arc length of a unit circle corresponding to the central angle measuring:(i) 30^{\circ}

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