Trig Ratio Table

Special angles comprise trigonometric values that may be considered exactly. The special angle values can be calculated using trigonometric ratios. Specifically, the angles of 0, 30, 45, 60, 90 degrees are the special ones. Right angles include the measure as 90 degree. A right triangle consists of a Right Angle as one of its 3 angles. The right triangles consist of two special triangles which are 30-60-90 right triangle and 45-45-90 right triangle. Let us see about the trig ratio table.

Trig Ratio Table

Followings are the six trigonometric ratios

Sin θ = `(opposite)/("hypotenuse")`

Cos θ = `(adjacent)/("hypotenuse")`

Tan θ = `(opposite)/(adjacent)`

Cosec θ = `("hypotenuse")/(opposite)`

Sec θ = `("hypotenuse")/(adjacent)`

Cot θ = `(adjacent)/(opposite)`

Trig ratio table

Example

Evaluate 46 sin 30˚ + 16 cos 60˚ - 8 tan 45˚

Solution

46 sin 30˚ + 16 cos 60˚ - 8 tan 45˚

46 x `1/2`   + 16 x `1/2`  - 8

23+ 8 -8

31 - 8 = 23

46 sin 30˚ + 16 cos 60˚ - 8 tan 45˚ = 23

Examples for Trig Ratio Table

Example 1 for trig ratio table

Find the adjacent side of the right angle triangle if angle θ is 60°, and the hypotenuse is 24.

Solution:

Cos θ =`(adjacent)/("hypotenuse")`

Given

Given θ is 60 degree

Hypotenuse side = 24

Assume adjacent side = x

Cos 600 =  `x/24`

x=   `24 xx cos 60^0`

x =  `24xx(1/2)`

x = 24 x 0.5        {Value of cos 60 degree`1/2` }

x = 12

Therefore, the adjacent side of the right angle triangle = 12

Example 2 for trig ratio table

Evaluate 18 sin 30˚ + 16 cos 60˚ - 8 tan 45˚

Solution

18 sin 30˚ + 16 cos 60˚ - 8 tan 45˚

18 x `1/2`   + 16 x `1/2`  - 8

9+ 8 -8

17 - 8 = 9

18 sin 30˚ + 16 cos 60˚ - 8 tan 45˚ = 9

Example 3 for trig ratio table

Evaluate 28 sin 30˚ + 16 cos 60˚ - 8 tan 45˚

Solution

28 sin 30˚ + 16 cos 60˚ - 8 tan 45˚

28 x `1/2`   + 16 x `1/2`  - 8

14+ 8 -8

22 - 8 = 14

28 sin 30˚ + 16 cos 60˚ - 8 tan 45˚ = 14

Example 4 for trig ratio table

Evaluate 12 cosec 30˚ + 16 sec 60˚ - 8 cot 45˚

Solution

12 cosec 30˚ + 16 sec 60˚ - 8 cot 45˚

12 x 2 + 16 x 2- 8

24+ 32 -8

56 - 8 = 48

12 cosec 30˚ + 16 sec 60˚ - 8 cot 45˚ = 48

Example 5 for trig ratio table

Evaluate 7 cosec 30˚ + 16 sec 60˚ - 8 cot 45˚

Solution

7 cosec 30˚ + 16 sec 60˚ - 8 cot 45˚

7 x 2 + 16 x 2- 8

14+ 32 -8

46 - 8 = 38

7 cosec 30˚ + 16 sec 60˚ - 8 cot 45˚ = 38