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2 votes
Find the exact value of sin 105 degrees​

User Hoang Dao
by
9.0k points

2 Answers

6 votes

Answer:


(√(6)+√(2))/(4)

Explanation:

I'm going to write 105 as a sum of numbers on the unit circle.

If I do that, I must use the sum identity for sine.


\sin(105)=\sin(60+45)


\sin(60)\cos(45)+\sin(45)\cos(60)

Plug in the values for sin(60),cos(45), sin(45),cos(60)


(√(3))/(2)(√(2))/(2)+(√(2))/(2)(1)/(2)


(√(3)√(2)+√(2))/(4)


(√(6)+√(2))/(4)

User Hluk
by
8.7k points
1 vote

Sin 105 degrees is equivalent to (√6 - √2) / 4.

The exact value of sin 105 degrees can be determined using trigonometric identities. Knowing that sin (90 + θ) = cos θ, we can rewrite sin 105 degrees as sin (90 + 15) degrees.

Applying the identity, sin (90 + 15) degrees equals cos 15 degrees.

Utilizing the trigonometric values of common angles, cos 15 degrees can be expressed as (√6 - √2) / 4.

This value is derived from trigonometric relationships, providing an exact representation of sin 105 degrees without resorting to decimal approximations.

User Marcos Dimitrio
by
7.9k points

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