Find the exact value of sin(285∘)
To find the exact value of sin(285°), we can use the sum and difference formulas for sine.
First, let's rewrite the angle 285° as the difference of two angles, 360° and 75°.
285° = 360° - 75°
Now, we can use the difference formula for sine:
sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
Let A = 360° and B = 75°:
sin(285°) = sin(360° - 75°)
We know that sin(360°) = 0 and cos(75°) = √3/2 based on the unit circle or trigonometric identities.
Plugging in these values into the formula:
sin(285°) = sin(360°)cos(75°) - cos(360°)sin(75°)
= 0 * (√3/2) - 1 * (√3/2)
= 0 - (√3/2)
= -√3/2
Therefore, the exact value of sin(285°) is -√3/2.
To find the exact value of sin(285∘), we can use the trigonometric identities and reference angles.
Step 1: Determine the reference angle.
Since the sine function is positive in the second quadrant, we can use the reference angle in the second quadrant, which is 180∘ - 285∘ = -105∘.
Step 2: Find the sine of the reference angle.
Since the reference angle is in the second quadrant, the sine function will be positive.
sin(-105∘) = sin(105∘)
Step 3: Use the sin(105∘) identity.
sin(105∘) = sin(180∘ - 105∘)
Step 4: Apply the difference of angles identity.
sin(180∘ - 105∘) = sin(75∘)
Step 5: Determine the exact value.
The exact value of sin(285∘) is sin(75∘).
use your half-angle formula to find sin(15°)
Now use your sum formula to find sin(270°+15°)