How do you find the exact values of sin 105 using the half angle formula?

Question

How do you find the exact values of sin 105 using the half angle formula?

1 Answer

Impact of this question

2973 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-15T17:04:12

Find sin 105.
Answer: #sin (105) = +- sqrt(2 + sqrt3)/2#

Explanation:

Call sin 105 = sin t
#cos (210) = cos (2t) = cos (30 + 180) = - cos (30) = (-sqrt3)/2#
Apply the trig identity: # cos 2a = 1 - 2sin^2 a.#
#cos 210 = (-sqrt3)/2 = 1 - 2sin^2 t#
#2sin^2 t = 1 + sqrt3/2 = (2 + sqrt3)/2#
#sin^2 t = (2 + sqrt3)/4 #-->

#sin t = +- sqrt(2 + sqrt3)/2#

Science

Math

Humanities

... and beyond

How do you find the exact values of sin 105 using the half angle formula?

1 Answer

Explanation:

Related questions

Impact of this question