How do you find the exact value of sin67.5 degrees?

Wade Bullock

Wade Bullock

Answered question

2022-07-15

How do you find the exact value of sin 67.5 degrees?

Answer & Explanation

Dalton Lester

Dalton Lester

Beginner2022-07-16Added 12 answers

67.5 2 = 1 2 ( 135 ) (Multiply 67.5 × 2)
The formula doesn't tell us whether sin 67.5 is positive or negative, but, since it is an acute angle we know that the sine is positive. (Be careful of the difference between "sign" and "sine").
We also need cos 135 . (That is the special angle that is 45 in Quadrant II.)
cos 135 = 2 2 .
Now use the formula ans simplify:
sin 67.5 = sin ( 1 2 ( 135 ) ) = 1 cos 135 2
= 1 ( 2 2 ) 2 = 1 + 2 2 2
= 2 + 2 4 = 2 + 2 2
sin 67.5 = 2 + 2 2
Cristopher Knox

Cristopher Knox

Beginner2022-07-17Added 6 answers

Call sin 67.5 = sin x
cos 2 x = cos 135 = 2 2 = 1 2 sin 2 x
2 sin 2 x = 1 + 2 2 = 2 + 2 2
sin 2 x = 2 + 2 4
sin x = sin 67.5 = 2 + 2 2

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