RS Aggarwal Solutions: Trigonometric Ratios (Exercise 8A) | Mathematics (Maths) Class 10 PDF Download

 Page 1


 
1. If sin 
3
2
, find the value of all T- ratios of 
Sol:
Now, we know that sin 
So, if AB = 
Now, using Pythagoras theorem, we have:
BC = k
Now, finding the other T-rations using their definitions, we get:
Cos 
Tan  
cot 
2. If cos 
7
25
, find the value of all T-ratios of 
Sol:
Now, we know that cos 
So, if BC = 7k, then AC = 25k, were k is a positive number.
Now, using Pythagoras theorem, we have:
Page 2


 
1. If sin 
3
2
, find the value of all T- ratios of 
Sol:
Now, we know that sin 
So, if AB = 
Now, using Pythagoras theorem, we have:
BC = k
Now, finding the other T-rations using their definitions, we get:
Cos 
Tan  
cot 
2. If cos 
7
25
, find the value of all T-ratios of 
Sol:
Now, we know that cos 
So, if BC = 7k, then AC = 25k, were k is a positive number.
Now, using Pythagoras theorem, we have:
 
AB = 24k
Now, finding the trigonometric ratios using their definitions, we get:
Sin 
Tan 
cot 
3. If tan
15
8
, find the values of all T-ratios of 
Sol:
Now, we know that tan =
So, if BC = 8k, then AB = 15k where k is positive number.
Now, using Pythagoras theorem, we have:
AC = 17k
Now, finding the other T-ratios using their definitions, we get:
Sin 
Cos 
cot 
4. If cot 2 find all the values of all T-ratios of 
Sol:
Now, we know that cot =
Page 3


 
1. If sin 
3
2
, find the value of all T- ratios of 
Sol:
Now, we know that sin 
So, if AB = 
Now, using Pythagoras theorem, we have:
BC = k
Now, finding the other T-rations using their definitions, we get:
Cos 
Tan  
cot 
2. If cos 
7
25
, find the value of all T-ratios of 
Sol:
Now, we know that cos 
So, if BC = 7k, then AC = 25k, were k is a positive number.
Now, using Pythagoras theorem, we have:
 
AB = 24k
Now, finding the trigonometric ratios using their definitions, we get:
Sin 
Tan 
cot 
3. If tan
15
8
, find the values of all T-ratios of 
Sol:
Now, we know that tan =
So, if BC = 8k, then AB = 15k where k is positive number.
Now, using Pythagoras theorem, we have:
AC = 17k
Now, finding the other T-ratios using their definitions, we get:
Sin 
Cos 
cot 
4. If cot 2 find all the values of all T-ratios of 
Sol:
Now, we know that cot =
 
So, if BC = 2k, then AB = k, is a positive number.
Now, using Pythagoras theorem, we have:
Now, finding the other T-ratios using their definitions, we get:
Sin =
Cos 
tan =
5. If cosec 10 find all the values of all T-ratios of 
Sol:
Now, we know that cosec =
So, if AC = (
Now, by using Pythagoras theorem, we have:
BC = 3k
Now, finding the other T-ratios using their definitions, we get:
tan =
cos =
sin =
Page 4


 
1. If sin 
3
2
, find the value of all T- ratios of 
Sol:
Now, we know that sin 
So, if AB = 
Now, using Pythagoras theorem, we have:
BC = k
Now, finding the other T-rations using their definitions, we get:
Cos 
Tan  
cot 
2. If cos 
7
25
, find the value of all T-ratios of 
Sol:
Now, we know that cos 
So, if BC = 7k, then AC = 25k, were k is a positive number.
Now, using Pythagoras theorem, we have:
 
AB = 24k
Now, finding the trigonometric ratios using their definitions, we get:
Sin 
Tan 
cot 
3. If tan
15
8
, find the values of all T-ratios of 
Sol:
Now, we know that tan =
So, if BC = 8k, then AB = 15k where k is positive number.
Now, using Pythagoras theorem, we have:
AC = 17k
Now, finding the other T-ratios using their definitions, we get:
Sin 
Cos 
cot 
4. If cot 2 find all the values of all T-ratios of 
Sol:
Now, we know that cot =
 
So, if BC = 2k, then AB = k, is a positive number.
Now, using Pythagoras theorem, we have:
Now, finding the other T-ratios using their definitions, we get:
Sin =
Cos 
tan =
5. If cosec 10 find all the values of all T-ratios of 
Sol:
Now, we know that cosec =
So, if AC = (
Now, by using Pythagoras theorem, we have:
BC = 3k
Now, finding the other T-ratios using their definitions, we get:
tan =
cos =
sin =
 
6. If sin 
2 2
2 2
a b
a b
find all the values of all T-ratios of 
Sol:
We have sin =
As,
Page 5


 
1. If sin 
3
2
, find the value of all T- ratios of 
Sol:
Now, we know that sin 
So, if AB = 
Now, using Pythagoras theorem, we have:
BC = k
Now, finding the other T-rations using their definitions, we get:
Cos 
Tan  
cot 
2. If cos 
7
25
, find the value of all T-ratios of 
Sol:
Now, we know that cos 
So, if BC = 7k, then AC = 25k, were k is a positive number.
Now, using Pythagoras theorem, we have:
 
AB = 24k
Now, finding the trigonometric ratios using their definitions, we get:
Sin 
Tan 
cot 
3. If tan
15
8
, find the values of all T-ratios of 
Sol:
Now, we know that tan =
So, if BC = 8k, then AB = 15k where k is positive number.
Now, using Pythagoras theorem, we have:
AC = 17k
Now, finding the other T-ratios using their definitions, we get:
Sin 
Cos 
cot 
4. If cot 2 find all the values of all T-ratios of 
Sol:
Now, we know that cot =
 
So, if BC = 2k, then AB = k, is a positive number.
Now, using Pythagoras theorem, we have:
Now, finding the other T-ratios using their definitions, we get:
Sin =
Cos 
tan =
5. If cosec 10 find all the values of all T-ratios of 
Sol:
Now, we know that cosec =
So, if AC = (
Now, by using Pythagoras theorem, we have:
BC = 3k
Now, finding the other T-ratios using their definitions, we get:
tan =
cos =
sin =
 
6. If sin 
2 2
2 2
a b
a b
find all the values of all T-ratios of 
Sol:
We have sin =
As,
 
7. If 15 cot A = 8 find all the values of sin A and sec A
Sol:
We have,
As,
1 17
sin 15 A
 
Sin A = 
15
17
Also,