Trigonometry Sine Function

In trigonometry one of the ratios is the sine function. It is defined by sinx = (Opposite side/Hypotenuse) = (Perpendicular/Hypotenuse)

This trigonometry sine function has applications on solving some practical problems in finding the height of the wall, length of a ladder leaning on the wall and the distance between the wall and the foot of the ladder.

Let us learn some sine values for standard angles.





The above table will help us in solving problems involving sine functions.  Now let us solve few problems on the topic trigonometry sine function.

Example Problems on Trigonometry Sine Function

Ex 1: From the below diagram, find the value of x using sine function.

Sol: Sin30 = `x/12`

This is implies, x = 12 `xx` sin30

                            = 12 `xx` `(1/2)` [table value for sin30 = `1/2` ]

                            = 6 cm.

Therefore, the value of x = 6cm.

Ex 2: From the below diagram, find the value of x using sine function.

Sol: Sin30 = `3/x`

               x = `3/sin30`

                  = `3/(1/2)`

                  = 3 `xx` 2 = 6cm.

Therefore, the value of x = 6cm.

Ex 3: If 2 sinA = 1, what is the value of A?

Sol: Given: 2sinA = 1

                     SinA = `1/2`

This implies that the value of A = `30^0` .     [Table value Sin30 = `1/2` ]

Ex 4: Simplify: sin60 + sin30.

Sol: sin60 + sin30 = `sqrt(3)/2` + `(1/2)`

                              = `(((sqrt(3)) + 1)/2)` .            [Table value Sin60 = `sqrt(3)/2` ]

Ex 5: In the triangle, find the value of x^0.

Sol: We know that Sin`x^0` = `sqrt (3)/2`

This implies `x^0` = `60^0` [Table value, sin60 = `sqrt (3)/2` ]

Ex 6: If 4sin²x – 3 = 0, x is an acute angle, find (i) sinx (ii) x.

Sol: Given: 4sin²x – 3 = 0

                     Sin²x = `(3/4)`

                     Sinx = `+-` `sqrt(3)/2`

(ii) Since, sinx = `+-` `sqrt(3)/2` ,

As per the table value, x =  `60^0` .

Therefore, x = `+-` `60^0` .

Ex 7: Solve for x:

Sin(x + 10) = ½

Sol: Since Sin(x + 10) = `(1/2)`

                        X + 10 = `30^0`

Therefore, x = 30 – 10

                     = `20^0` .

Therefore, the value of x = `20^0` .

Practice Problems on Trigonometry Sine Function

1. Solve for x: Sin² x + sin²30 = 1.

[Answer: x = `+-` `60^0` ]

2. Find the acute angle A and B, if Sin (A+B) = 1 and Sin(A – B) = `(1/2)`

[Answer: A = `60^0` , B =` 30^0` ].