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 0 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 θ Sin θ 0 1 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