151k views
0 votes
Find the exact value, without a

calculator.
570
570
sin
6
sin
12
2
'?]+/

Find the exact value, without a calculator. 570 570 sin 6 sin 12 2 '?]+/-example-1
User Minh Pham
by
8.3k points

1 Answer

5 votes

Answer:

√(2 + √3)/4

Explanation:

Sine 5π/12 = Sine (5π/6)/2

Recall

π = 180°

Thus,

Sine (5π/6)/2 = Sine (5×180 /6)/2

= Sine 150/2

Recall

Sine θ/2 = √(1 – Cos θ)/2

Thus,

Sine 150/2 = √(1 – Cos 150)/2

But, Cosine is negative in the 2nd quadrant. Thus,

Cos 150 = – Cos 30 = –√3/2

Thus,

√(1 – Cos 150)/2 = √(1 – –√3/2 )/2

= √(1 + √3/2 )/2

= √[(2 + √3)/2 ÷ 2]

= √[(2 + √3)/2 × 1/2]

= √(2 + √3)/4

Therefore,

Sine 5π/12 = √(2 + √3)/4

User Rdchambers
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories