Question

Find the two angles that satisfy the equation.

3a. sin(3x + 2)° = cos(x + 44)º.

3b. sin(2x + 20)° = cos(3x + 30)".

Answer 1

3a. 35°, 55° 3b. 36°, 54°

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°