**1. Find out the value of the following:**

**(i) sin 35**

^{o}22′**Solution:-**

^{o}22’,

^{o}

^{o}22’ is obtained as under,

^{o}22’ = 0.5779 … [from table]

^{o}22’ = 0.5789

**(ii) sin 71**

^{o}31′**Solution:-**

^{o}31’,

^{o}

^{o}31’ is obtained as under,

^{o}31’ = 0.9483 … [from table]

^{o}31’ = 0.9484

**(iii) sin 65**

^{o}20′**Solution:-**

^{o}20’,

^{o }

^{o}20’ is obtained as under,

^{o}20’ = 0.0985 … [from table]

^{o}20’ = 0.9087

**(iv) sin 23**

^{o}56′**Solution:-**

^{o}56’,

^{o}

^{o}56’ is obtained as under,

^{o}56’ = 0.4051 … [from table]

^{o}56’ = 0.4056

**2. Find out the value of the following:**

**(i) cos 62**

^{o}27′**Solution:-**

^{o}27’,

^{o}

^{o}27’ is 0.4625.

**(ii) cos 3° 11′**

**Solution:-**

^{o}11′,

^{o}

^{o}11′ is 0.9984.

**(iii) cos 86**

^{o}40′**Solution:-**

^{o}

**(iv) cos 45**

^{o}58′.**Solution:-**

^{o}58′,

^{o}

**3. Find out the value of the following :**

**(i) tan 15**

^{o}2′**Solution:-**

^{o}2′,

^{o}

^{o}2’ is 0.2685.

**(ii) tan 53**

^{o}14′**Solution:-**

^{o}14′,

^{o}In the vertical column headed by 14’ i.e. 14’ – 12’ = 2’ in the difference column, the value of 2’ in mean difference column is 16.

^{o}14′ is 1.3383.

**(iii) tan 82**

^{o}18′**Solution:-**

^{o}18′,

^{o}

^{o}18’ is 7.3962

**(iv) tan 6**

^{o}9′.**Solution:-**

^{o}9′,

^{o}

^{o}9′ is 0.1078.

**4. Use tables to find out the acute angle θ, given that:**

**(i) sin θ = .5789**

**Solution:-**

^{o}and in the column headed by 18’ and in the mean difference,we see .

^{o}18’ + 4’

^{o}22’

**(ii) sin θ = .9484**

**Solution:-**

^{o}and in the column headed by 30’ and in the mean difference, we see .9484 - .9483 = .0001 in the column of 1’.

^{o}30’ + 1’

^{o}31’.

**(iii) sin θ = .2357**

**Solution:-**

^{o}and in the column headed by 36’ and in the mean difference, we see .2357 - .2351 = .0006 in the column of 2’.

^{o}36’ + 2’ = 13

^{o}38’

**(iv) sin θ = .6371.**

**Solution:-**

^{o}and in the column headed by 30’ and in the mean difference, we see .6371 - .6361 = .0010 in the column of 4’.

^{o}30’ + 4’ = 39

^{o}34’.

**5. Use the tables to find out the acute angle θ, given that:**

**(i) cos θ = .4625**

**Solution:-**

^{o}and in the column headed by 30’ and in the mean difference, we see .4625 - .4617 = .0008 in the column of 3’.

^{o}30’ - 3’

^{o}27’.

**(ii) cos θ = .9906**

**Solution:-**

^{o}and in the column headed by 54’ and in the mean difference,

^{o}54’ - 3’ = 70

^{o}51’.

**(iii) cos θ = .6951**

**Solution:-**

^{o}and in the mean difference, we see .

^{o}’ - 2’ = 45

^{o}58’.

**(iv) cos θ = .3412.**

**Solution:-**

^{o}and in the column headed by 6’ and in the mean difference,

^{o}6’ - 3’ = 70

^{o}3’.

**6. Use tables to find out the acute angle θ, given that:**

**(i) tan θ = .2685**

**Solution:-**

^{o}and in the mean difference,

^{o}+ 2’ = 15

^{o}2’.

**(ii) tan θ = 1.7451**

**Solution:-**

^{o}6’ + 5’ = 60

^{o}11’.

**(iii) tan θ = 3.1749**

**Solution:-**

^{o}and in the column headed by 30’ and in the mean difference, we see 3.1749 - 3.1716 = .0033 in the column of 1’. Then we get,

^{o}30’ + 1’ = 72

^{o}31’.

**(iv) tan θ = .9347**

**Solution:-**

^{o}and in the mean difference, we see .9347 - .9325 = .0022

^{o}+ 4’ = 43

^{o}4’.

**7. Using trigonometric table, find out the measure of the angle A when sin A = 0.1822.**

**Solution:-**

^{o}and in the column headed by 30’.

^{o}30’

**8. Using tables, find out the value of 2 sin θ – cos θ when (i) θ = 35° (ii) tan θ = .2679.**

**Solution:-**

^{o }

^{o}

^{o}= .5736 and cos 35

^{o}

**(ii) from the question it is given that, tan θ = .2679**

^{o}.

^{o }

^{o}– cos 15

^{o}

^{o}= .2588 and cos 15

^{o}= .9659

**9. If sin x° = 0.67, find the value of (i) cos x° (ii) cos x° + tan x°.**

**Solution:-**

^{o}and in the mean difference,

^{o}+ 4’ = 42

^{o}4’.

**(i) cos xo = cos 42**

^{o}4′**(ii) cos x**

^{o}+ tan x° = cos 42° 4′ + tan 42° 4′

**10. If θ is acute and cos θ = .7258, find out the value of (i) θ (ii) 2 tan θ – sin θ.**

**Solution:-**

^{o}28’.

**(ii) 2 tan θ – sin θ**