trigonometry1

Start Your Free Trial

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

Expert Answers info

Rylan Hills eNotes educator | Certified Educator

calendarEducator since 2010

write12,544 answers

starTop subjects are Math, Science, and Business

The exact value of sin(60+210) is required. sin (60 + 210) =...

(The entire section contains 33 words.)

Unlock This Answer Now


check Approved by eNotes Editorial


giorgiana1976 | Student

This problem requests the use of 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.

check Approved by eNotes Editorial