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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 order 0° 30° 45° 60° 90° Put down the number 0, 1, 2, 3, 4 0 1 2 3 4 Divide each number by 4 04 14 24 34 44 Take Square roots √ 0 / 4 √ 1 / 4 √ 2 / 4 √ 3 / 4 √ 4 / 4 Simplify and we get value of Sin θ Sin θ 0 12 1√2 √3  2 1 Values in reverse order are those of Cos θ Cos θ 1 √3  2 1√2 12 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