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Class 10 Math Intoduction to Geometry 1. Find A when.(ii) l=4.5 \mathrm{~m} r=2.5 \mathrm{~m}


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1. Find A when.(ii) l=4.5 \mathrm{~m} r=2.5 \mathrm{~m}

4. Express the following angles into radians.(viii) 315^{\circ}
4. Express the following angles into radians.(viii)  315^{\circ}

4. Express the following angles into radians.(viii) 315^{\circ}

1. Locate the following angles:(vii) -150^{\circ}
1. Locate the following angles:(vii)  -150^{\circ}

1. Locate the following angles:(vii) -150^{\circ}

Example: Locate each angle in standard position.(iii) -270^{\circ}
Example: Locate each angle in standard position.(iii)  -270^{\circ}

Example: Locate each angle in standard position.(iii) -270^{\circ}

2. Identify the closest rantal angles between which the following angles lies.(iii) 572^{\circ}
2. Identify the closest rantal angles between which the following angles lies.(iii)  572^{\circ}

2. Identify the closest rantal angles between which the following angles lies.(iii) 572^{\circ}

In problems 7-24 verify the identities.21. \sin ^{3} \theta=\sin \theta-\sin \theta \cos ^{2} \theta
In problems  7-24  verify the identities.21.  \sin ^{3} \theta=\sin \theta-\sin \theta \cos ^{2} \theta

In problems 7-24 verify the identities.21. \sin ^{3} \theta=\sin \theta-\sin \theta \cos ^{2} \theta

Example 1: A flagpole 17.9 meter high casts a 7 meter shadow Find the angle of elevation of the sun.
Example 1: A flagpole  17.9  meter high casts a 7 meter shadow Find the angle of elevation of the sun.

Example 1: A flagpole 17.9 meter high casts a 7 meter shadow Find the angle of elevation of the sun.

2. Write short answers of the following questions.(v) Convert \frac{\pi}{4} radians to degree measure.
2. Write short answers of the following questions.(v) Convert  \frac{\pi}{4}  radians to degree measure.

2. Write short answers of the following questions.(v) Convert \frac{\pi}{4} radians to degree measure.

5. Fill in the blanks.(i) \cos \left(-150^{\circ}\right)=\ldots \ldots \ldots \cos 150^{\circ} (ii) \sin \left(-310^{\circ}\right)= (iii) \tan \left(-210^{\circ}\right)=\ldots \ldots \ldots \tan 210^{\circ} (iv) \cot \left(-45^{\circ}\right)=\ldots \ldots \ldots \cot 45^{\circ} (v) \sec \left(-60^{\circ}\right)=\ldots \ldots \ldots \sec 60^{\circ} (vi) \operatorname{cosec}\left(-137^{\circ}\right)=
5. Fill in the blanks.(i)  \cos \left(-150^{\circ}\right)=\ldots \ldots \ldots \cos 150^{\circ} (ii)  \sin \left(-310^{\circ}\right)= (iii)  \tan \left(-210^{\circ}\right)=\ldots \ldots \ldots \tan 210^{\circ} (iv)  \cot \left(-45^{\circ}\right)=\ldots \ldots \ldots \cot 45^{\circ} (v)  \sec \left(-60^{\circ}\right)=\ldots \ldots \ldots \sec 60^{\circ} (vi)  \operatorname{cosec}\left(-137^{\circ}\right)=

5. Fill in the blanks.(i) \cos \left(-150^{\circ}\right)=\ldots \ldots \ldots \cos 150^{\circ} (ii) \sin \left(-310^{\circ}\right)= (iii) \tan \left(-210^{\circ}\right)=\ldots \ldots \ldots \tan 210^{\circ} (iv) \cot \left(-45^{\circ}\right)=\ldots \ldots \ldots \cot 45^{\circ} (v) \sec \left(-60^{\circ}\right)=\ldots \ldots \ldots \sec 60^{\circ} (vi) \operatorname{cosec}\left(-137^{\circ}\right)=

4. In which rant \theta lie when(v) \operatorname{cosec} \theta>0 \cos \theta>0
4. In which rant  \theta  lie when(v)  \operatorname{cosec} \theta>0 \cos \theta>0

4. In which rant \theta lie when(v) \operatorname{cosec} \theta>0 \cos \theta>0

(a)(b)
(a)(b)

(a)(b)

3. Find r when:(i) l=4 \mathrm{~cm} \theta=\frac{1}{4} radians
3. Find  r  when:(i)  l=4 \mathrm{~cm} \theta=\frac{1}{4}  radians

3. Find r when:(i) l=4 \mathrm{~cm} \theta=\frac{1}{4} radians

Example: Locate(b) 120^{\circ}
Example: Locate(b)  120^{\circ}

Example: Locate(b) 120^{\circ}

Example 1:(ii) Convert 32.25^{\circ} to D^{\circ} M^{\prime} S^{\prime \prime} form.
Example 1:(ii) Convert  32.25^{\circ}  to  D^{\circ} M^{\prime} S^{\prime \prime}  form.

Example 1:(ii) Convert 32.25^{\circ} to D^{\circ} M^{\prime} S^{\prime \prime} form.

1. Locate the following angles:(iii) 135^{\circ}
1. Locate the following angles:(iii)  135^{\circ}

1. Locate the following angles:(iii) 135^{\circ}

In problems 7-24 verify the identities.14. \frac{\sin ^{2} \theta}{\cos \theta}+\cos \theta=\sec \theta
In problems  7-24  verify the identities.14.  \frac{\sin ^{2} \theta}{\cos \theta}+\cos \theta=\sec \theta

In problems 7-24 verify the identities.14. \frac{\sin ^{2} \theta}{\cos \theta}+\cos \theta=\sec \theta

3. Fill in the blanks(i) \pi radians = (ii) The terminal side of angle 235^{\circ} lies in(iii) Terminal side of the angle -30^{\circ} lies in(iv) Area of a circular sector is(v) If r=2 \mathrm{~cm} and \theta=3 radians then area of the circular sector is(vi) The general form of the angle 480^{\circ} is(vii) If \sin \theta=\frac{1}{2} then \theta= (viii) If \theta=300^{\circ} then \sec (-300)^{\circ}= (ix) 1+\cot ^{2} \theta= (x) \operatorname{Sec} \theta-\tan \theta=
3. Fill in the blanks(i)  \pi  radians  = (ii) The terminal side of angle  235^{\circ}  lies in(iii) Terminal side of the angle  -30^{\circ}  lies in(iv) Area of a circular sector is(v) If  r=2 \mathrm{~cm}  and  \theta=3  radians then area of the circular sector is(vi) The general form of the angle  480^{\circ}  is(vii) If  \sin \theta=\frac{1}{2}  then  \theta= (viii) If  \theta=300^{\circ}  then  \sec (-300)^{\circ}= (ix)  1+\cot ^{2} \theta= (x)  \operatorname{Sec} \theta-\tan \theta=

3. Fill in the blanks(i) \pi radians = (ii) The terminal side of angle 235^{\circ} lies in(iii) Terminal side of the angle -30^{\circ} lies in(iv) Area of a circular sector is(v) If r=2 \mathrm{~cm} and \theta=3 radians then area of the circular sector is(vi) The general form of the angle 480^{\circ} is(vii) If \sin \theta=\frac{1}{2} then \theta= (viii) If \theta=300^{\circ} then \sec (-300)^{\circ}= (ix) 1+\cot ^{2} \theta= (x) \operatorname{Sec} \theta-\tan \theta=

2. Write short answers of the following questions.(iii) How many minutes are there in two right angles?
2. Write short answers of the following questions.(iii) How many minutes are there in two right angles?

2. Write short answers of the following questions.(iii) How many minutes are there in two right angles?

2. Find l when:(i) \theta=180^{\circ} r=4.9 \mathrm{~cm}
2. Find  l  when:(i)  \theta=180^{\circ} r=4.9 \mathrm{~cm}

2. Find l when:(i) \theta=180^{\circ} r=4.9 \mathrm{~cm}

4. Express the following angles into radians.(ii) (60)^{\circ}
4. Express the following angles into radians.(ii)  (60)^{\circ}
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4. Express the following angles into radians.(ii) (60)^{\circ}

2. Write short answers of the following questions.(iv) Define radian measure of an angle.
2. Write short answers of the following questions.(iv) Define radian measure of an angle.
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2. Write short answers of the following questions.(iv) Define radian measure of an angle.

2. Identify the closest rantal angles between which the following angles lies.(i) 156^{\circ}
2. Identify the closest rantal angles between which the following angles lies.(i)  156^{\circ}
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2. Identify the closest rantal angles between which the following angles lies.(i) 156^{\circ}

1. Find A when.(ii) l=4.5 \mathrm{~m} r=2.5 \mathrm{~m}
1. Find  A  when.(ii)  l=4.5 \mathrm{~m} r=2.5 \mathrm{~m}
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1. Find A when.(ii) l=4.5 \mathrm{~m} r=2.5 \mathrm{~m}

5. Convert each of following to degrees.(iii) \frac{7 \pi}{8}
5. Convert each of following to degrees.(iii)  \frac{7 \pi}{8}
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5. Convert each of following to degrees.(iii) \frac{7 \pi}{8}

In problems 7-24 verify the identities.22. \cos ^{4} \theta-\sin ^{4} \theta=\left(\cos ^{2} \theta-\sin ^{2} \theta\right)
In problems  7-24  verify the identities.22.  \cos ^{4} \theta-\sin ^{4} \theta=\left(\cos ^{2} \theta-\sin ^{2} \theta\right)
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In problems 7-24 verify the identities.22. \cos ^{4} \theta-\sin ^{4} \theta=\left(\cos ^{2} \theta-\sin ^{2} \theta\right)

12. Find the values of the trigonometric functions. Do not use trigonometric tables or calculator.(ii) \tan 330^{\circ}
12. Find the values of the trigonometric functions. Do not use trigonometric tables or calculator.(ii)  \tan 330^{\circ}
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12. Find the values of the trigonometric functions. Do not use trigonometric tables or calculator.(ii) \tan 330^{\circ}

12. Find the values of the trigonometric functions. Do not use trigonometric tables or calculator.(vii) \cos \left(-450^{\circ}\right)
12. Find the values of the trigonometric functions. Do not use trigonometric tables or calculator.(vii)  \cos \left(-450^{\circ}\right)
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12. Find the values of the trigonometric functions. Do not use trigonometric tables or calculator.(vii) \cos \left(-450^{\circ}\right)

6. The given point P lies on the terminal side of \theta . Find rant of \theta and all six trigonometric ratios.(ii) (-3-4)
6. The given point  P  lies on the terminal side of  \theta . Find rant of  \theta  and all six trigonometric ratios.(ii)  (-3-4)
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6. The given point P lies on the terminal side of \theta . Find rant of \theta and all six trigonometric ratios.(ii) (-3-4)

5. Convert each of following to degrees.(v) 3
5. Convert each of following to degrees.(v) 3
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5. Convert each of following to degrees.(v) 3

11. Find the values of trigonometric functions at the indicated angle \theta in the right triangle.
11. Find the values of trigonometric functions at the indicated angle  \theta  in the right triangle.
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11. Find the values of trigonometric functions at the indicated angle \theta in the right triangle.

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