# Find the exact value of the expression sin(60+210).

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the exact value of sin (60 + 210)

sin (60 + 210)

=> sin 270

=> sin (360 - 90)

Now sin (360 - 90)= -sin 90

=> - sin 90

As sin 90 = 1

=> - sin 90

=> -1

Therefore sin (60 + 210) = -1.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine the exact value of the sum of the angles, we'll apply the formula:

sin (a+b) = sin a*cos b + sin b*cos a

sin(60+210) = sin 60*cos 210 + sin 210*cos 60

We notice that 210 = 180 + 30

So, the values of the sine and cosine functions of the angle 210 will be the values of the angle of 30 degrees. We notice that 210 is located in the 3rd quadrant, so the values of the sine and cosine functions are both negative.

sin 210 = - sin 30 = -1/2

cos 210 = - cos 30 = -sqrt3/2

sin(60+210) = sin 60*(- sin 30) + (- cos 30)*cos 60

sin(60+210) = - sqrt3/4 - sqrt3/4

sin(60+210) = -sqrt3/2

sin(60+210) = -0.8660 approx.