If sin θ = 1/2, then θ equals:
A90°
B45°
C60°
D30°
Answer & Solution
Correct answer: D. 30°
To find the value of $\theta$ given $\sin \theta = 1/2$, we refer to the trigonometric ratios of special angles (30°, 45°, and 60°).
1. **Recall the definition**: In a right-angled triangle, $\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}$.
2. **Special Triangle Analysis**: Consider a $30^\circ-60^\circ-90^\circ$ triangle. In this triangle, if the hypotenuse is $2$, the side opposite to the $30^\circ$ angle is $1$.
3. **Applying the ratio**:
$$\sin 30^\circ = \frac{1}{2}$$
4. **Comparison**: Since the problem states $\sin \theta = 1/2$, by comparing this to our known values, we conclude that $\theta = 30^\circ$.
Therefore, the correct option is **D**.
Keep practising Introduction to Trigonometry
Browse all Introduction to Trigonometry questions for Andhra Pradesh SSC (Class 10), or explore more Mathematics topics.
Related questions
CLASS10 · Mathematics · Heights & Distances — Solve in OrderCLASS10 · Mathematics · Standard Angle ValuesCLASS10 · Mathematics · Trigonometric RatiosAngle of depression is measured from:If a tower 30 m tall casts a shadow of 30 m, the angle of elevation of the sun is:The identity sin²θ + cos²θ equals:The value of sin 30° is:Prove or evaluate: (1 + tan²A)(1 − sin²A).