Use a sum or difference identity to find the exact value of sin225°
a. (-√2 - √6)/4
b. (√6 - √2)/4
c. (√6 + √2)/4
d. (√2 - √6)/4
is it A?
a) is the sine of 285
b) is the sine of 15, 165
c) is the sine of 75, 105
d) is the sine of -15, 195
check my thinking.
it's B?
none of the given answers is correct.
Are you sure you typed it correctly?
sin 225 = sin(180+45)
= sin180cos45 + cos180sin45
= 0 + (-1)√2/2
= -√2/2
no those are the options for sure :/
Are you sure it is not
> Use a sum or difference identity to find the exact value of sin255
To find the exact value of sin225° using a sum or difference identity, we can use the identity:
sin(A ± B) = sinA * cosB ± cosA * sinB
In this case, we can express 225° as the sum of two angles: 180° and 45°. So, we have:
sin225° = sin(180° + 45°)
Using the sum identity, we can rewrite this as:
sin225° = sin 180° * cos 45° + cos 180° * sin 45°
Because sin 180° = 0 and cos 180° = -1, we can simplify this further:
sin225° = 0 * cos 45° + (-1) * sin 45°
= -sin 45°
Since sin 45° can be written as √2 / 2, we have:
sin225° = -√2 / 2
Therefore, the correct answer is not option A.