Question

4sin450* + 3cos120* +7sin390* = ?

Answer 1

4sin(450*) + 3cos(120*) + 7sin390*) = 4sin(360* + 90*) + 3cos(180* - 60*) + + 7sin(360* + 30*) = 4sin90* - 3cos60* + sin30* = 4*1 - 3*(1/2) + 1/2 = 3

Answer 2

To solve this expression, let's break it down step by step:

1. Start by converting the angles from degrees to radians:

   • 450 degrees = (450 * π) / 180 radians = (5π / 2) radians
   • 120 degrees = (120 * π) / 180 radians = (2π / 3) radians
   • 390 degrees = (390 * π) / 180 radians = (13π / 6) radians

2. Apply the trigonometric identities:

   • sin(x) = sin(-x)
   • cos(x) = cos(-x)

Now, let's calculate the expression:

4sin(450*) + 3cos(120*) + 7sin(390*)

= 4sin(5π/2) + 3cos(2π/3) + 7sin(13π/6)

Since sin(5π/2) = sin(-π/2) = -1 and cos(2π/3) = cos(-2π/3), we can rewrite the expression as:

= 4(-1) + 3cos(-2π/3) + 7sin(13π/6)

Now, let's calculate cos(-2π/3) and sin(13π/6):

cos(-2π/3) = cos(2π/3) = 1/2 sin(13π/6) = sin(π/6) = 1/2

Substituting these values back into the expression:

= 4(-1) + 3(1/2) + 7(1/2)

= -4 + 3/2 + 7/2

= -4 + 5/2

= -8/2 + 5/2

= -3/2

Therefore, 4sin(450*) + 3cos(120*) + 7sin(390*) is equal to -3/2.