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Home >> Trigonometry Ratios >> T Ratios of Angles - 30, 45, 60 & 90 degree angles >>

T Ratios of Angles - 30, 45, 60 & 90 degree angles in Trigonometry

T Ratios of Angles - 30, 45, 60 & 90 degree angles Find Height, Distance using T - Ratios

Table for T ratios of 0°, 30°, 45° 60° 90°

Write down the angles in order30°45°60°90°
Put down the number 0, 1, 2, 3, 4 01234
Divide each number by 40
4
1
4
2
4
3
4
4
4
Take Square roots 0 / 4  1 / 4  2 / 4  3 / 4  4 / 4 
Simplify and we get value of Sin θSin θ01
2
  1
2
3
  2
1
Values in reverse order are those of Cos θ Cos θ 1 3
  2
  1
2
1
2
0
Divide values of Sin θ by those of Cos θ Tan Θ 0   1
 3 
1  3 
Take reciprocals of the values of Tan θ Cot θ  3  1  1
 3 
0
Take reciprocals values of Cos θ Sec θ 1   2  
 3 
 2  2
Rake reciprocals of the values of Sin θ Cosec θ 2  2   2  
 3 
1


Let's try out some examples using the above table

Example - 1 : Find Cosec2 30° Sin2 - 45° - Sec2 60°
Solution : According to T ratio table the cosec, sin and sec degree values are

Cosec 30° = 2

Sin 45° =    1  
 2 


Sec 60° = 2

we get the following equation

= (2)2 x ( 1 /  2  )2 - (2)2

4 x 1
2
- 4


= 2 - 4 = -2




Example - 2 : Find sin 30° cos 45° + cos 30° sin 45°
Solution - According to T ratio table the sin, cos degree values are

Sin 30° = 1
2


Cos 45° =    1  
 2 


Sin 45° =    1  
 2 


we get the following equation

1
2
x    1   
 2 
+  3 
   2
x    1   
 2 


   1   
2 √ 2 
+  3 
2 √ 2 


1 +  3 

  2 √ 2 



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