0580/43 May/Jun 2023, Question 7: Trigonometric Graphs and Equations

Part (a) · 1 mark

Choose which word from the list correctly names the type of function shown by the given curve.

1. 1The curve has two turning points and goes from bottom left to top right
2. 2It is a cubic

Answercubic

Part (bi) · 2 marks

Sketch the curve y = 1/(2x), for x not equal to 0, on the blank axes provided.

1. 1For x > 0, y is positive and decreases towards 0; for x < 0, y is negative
2. 2Draw two branches in quadrants 1 and 3 approaching the axes (asymptotes x = 0 and y = 0)

AnswerReciprocal curve: one branch in the first quadrant and one in the third, approaching both axes without crossing them

Part (bii) · 2 marks

Solve the equation 1/(2x) = 2x for x.

1. 11 = 2x × 2x
2. 24x² = 1
3. 3x² = 1/4
4. 4x = 1/2 and x = −1/2

Answerx = 1/2 and x = −1/2

Part (ci) · 2 marks

Sketch y = sin x over the interval 0° to 360° on the given axes.

1. 1Start at (0, 0), rise to maximum 1 at 90°
2. 2Back to 0 at 180°, down to minimum −1 at 270°
3. 3Back to 0 at 360°

AnswerSine curve through (0, 0), (180, 0) and (360, 0) with maximum 1 at 90° and minimum −1 at 270°

Part (cii) · 3 marks

Solve 3 sin x + 1 = 0 for angles between 0° and 360°.

1. 1sin x = −1/3
2. 2sin⁻¹(1/3) = 19.47°
3. 3x = 180 + 19.47 = 199.5°
4. 4x = 360 − 19.47 = 340.5°

Answer199.5 or 199.47… and 340.5…

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