(a) Copy and complete the table of values for the relation (y = 2 sin x + 1)
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° | 240° |
270° |
| y | 1.0 | 2.7 | 0.0 | -0.7 |
(b) Using scales of 2 cm to 30° on the x- axis and 2 cm to 1 unit on the y- axis, draw the graph of (y = 2 sin x + 1, 0° leq x leq 270°).
(c) Use the graph to find the values of x for which (sin x = frac{1}{4}).
Explanation
(a)
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° | 240° |
270° |
| y | 1.0 | 2.0 | 2.7 | 3.0 | 2.7 | 2.0 | 1.0 | 0.0 | -0.7 | -1.0 |
(b)
(c) (sin x = frac{1}{4}) (Given)
Multiply through by 2 ; (2 sin x = 2 times frac{1}{4} = frac{1}{2})
(2 sin x = frac{1}{2} implies 2 sin x – frac{1}{2} = 0)
Add (1frac{1}{2}) to both sides ;
(2 sin x – frac{1}{2} + 1frac{1}{2} = 0 + 1frac{1}{2})
(implies 2 sin x + 1 = 1frac{1}{2})
Draw the line (y = 1frac{1}{2}) on the same axis as (y = 2 sin x + 1). The line (y = 1frac{1}{2}) cuts the curve at points P and Q where x = 15° and x = 168°. Hence, the values of x for which (sin x = frac{1}{4})are 15° and 168°.