Test Index

JAMB Mathematics 2023 Paper

Question : 76

Total: 80

Use the graph of sin (θ) above to estimate the value of θ when sin (θ) = -0.6 for $0^{\circ} \leq \theta \leq 360^{\circ}$

Solution:

Concept:

Use the sine graph scale to read the angles where

\sin(\theta) = -0.6

between

0^{\circ}

and

360^{\circ}

Explanation:

On the

y

-axis, each small box represents

0.2

, so

-0.6

3

boxes below zero.

On the

x

-axis, each small box represents

\frac{90^{\circ}}{6} = 15^{\circ}

For the first angle, count

2.5

boxes after

180^{\circ}

\theta_1 = 180^{\circ} + (2.5 \times 15^{\circ}) = 217.5^{\circ} \approx 218^{\circ}

For the second angle, count

3.5

boxes after

270^{\circ}

\theta_2 = 270^{\circ} + (3.5 \times 15^{\circ}) = 322.5^{\circ} \approx 323^{\circ}

Thus, the required angles are

218^{\circ}

and

323^{\circ}

Answer:

\theta = 218^{\circ}, 323^{\circ}

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