Find the two angles that satisfy the equation.

3a. sin(3x + 2)° = cos(x + 44)º.

3b. sin(2x + 20)° = cos(3x + 30)".

3a. 35°, 55°     3b. 36°, 54°

Step-by-step explanation:

3a. sin(3x + 2)° = cos(x+44)°

Since sine and cosine are based upon right triangles, the two angles must add up to 90°. Thereby, 3x+2 +  x+44 = 90. Combine like terms to get:

4x + 46  =  90       subtract 46 from both sides

   -46     -46

4x          = 44        divide both sides by 4

4                4

x    =   11          plug that back into both angles

3(11) + 2 = 35°;   11 + 44 = 55°

3b. In your equation, (2x+20) + (3x+30) = 90. Combining like terms gives you:

5x + 50  =  90     subtract 50 from both sides

     - 50     -50

5x  =  40        divide both sides by 5

5         5

x   =  8      plug that back into both angles

2x+20 = 2(8) + 20 = 36°

3x+30 = 3(8) + 30  = 54°

The two angles are 36° and 54°

triangle and cube

step-by-step explanation: