How can I find the exact value of Sin 480 degrees? Thanks
Sin(480) = sin (5x90 + 30) = cos 30 = sqrooy(3)/2
Sin(360+120)
Sin 120
Sin (90+30)
+cos 30
3/2
To find the exact value of sine (sin) 480 degrees, we need to use knowledge of the unit circle and the periodicity of the sine function.
1. Start by recognizing that the sine function repeats itself every 360 degrees. So, we can subtract multiples of 360 from 480 to bring it within the first 360-degree range: 480 - 360 = 120 degrees.
2. Next, draw a unit circle and mark the angle of 120 degrees.
3. In the unit circle, the y-coordinate of the point where the angle intercepts the unit circle represents the sine value of that angle. Since sine is positive in the first and second quadrants, we can determine the value will be positive.
4. Determine the exact value of sin 120 degrees. In a 30-60-90 triangle, the sine value of 30 degrees is 1/2, and the sine value of 60 degrees is √3/2. Since 120 degrees is in the second quadrant, the value will be positive √3/2.
Therefore, the exact value of sin 480 degrees is √3/2.
Thank you I see where I got stuck
3/2
480°=360°+120°
sin(480°)=sin(120°)
sin(90°+x)=sin(90°-x)
sin(90°+30°)=sin(90°-30°)
sin(120°)=sin(60°)
sin(480°)=sin(120°)=sin(60°)=sqroot(3)/2