If \(cos x = \frac{3}{5}\), then find the value of sin x – sin3 x.
1. 0.476
2. 0.288
3. 0.358
4. 0.389
1. 0.476
2. 0.288
3. 0.358
4. 0.389
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Correct Answer – Option 2 : 0.288
Given:
Cos x = 3/5
Formula used:
Sin x = perpendicular/hypotenuse,
Cos x = base/hypotenuse,
By Pythagoras theorem,
Hypotenuse2 = Perpendicular2 + Base2
Calculation:
According to the question:
Cos x = 3/5
Base = 3
⇒ Hypotenuse = 5
Hypotenuse2 = Perpendicular2 + Base2
⇒ 52 = 32 + Perpendicular2
⇒ 25 = 9 + Perpendicular2
⇒ 25 – 9 = Perpendicular2
⇒ Perpendicular2 = 16
⇒ Perpendicular = √16
⇒ Perpendicular2 = √(4 × 4)
⇒ Perpendicular = 4
Now,
(Sin x – Sin3 x)
⇒ [(perpendicular/hypotenuse) – (perpendicular/hypotenuse)3]
⇒ [4/5 – (4/5)3]
⇒ [4/5 – 64/125]
⇒ (100 – 64)/125
⇒ 36/125 = 0.288
∴ The answer is 0.288.