Theory question 107
Trigonometry(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 for 0° ≤ x ≤ 270°.
(c) Use the graph to find the values of x for which sin x = ¼.
Show the model answer
Model answer
(a) 30°: 2.0; 60°: 2.7; 90°: 3.0; 150°: 2.0; 180°: 1.0; 270°: −1.0.
(b) Plot the points and draw a smooth curve.
(c) sin x = ¼ means 2 sin x + 1 = 1.5. Draw y = 1.5: x ≈ 15° and x ≈ 165°.
Explanation
Change the equation so it matches the graph: 2(¼) + 1 = 1.5.