Question

Consider the following statements :
1. If $3\theta$ is an acute angle such that $\sin 3\theta =\cos 2\theta$, then the measurement of $\theta$ in radian equals to $\frac{\pi }{10}$.
2. One radian is the angle subtended at the centre of a circle by an arc of the same circle whose length is equal to the diameter of that circle.
Which of the above statements is/are correct ?

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2

Answer 1

Answer: (A)

1 only

Statement 1-

$sin3\theta =cos2\theta$

$\Rightarrow sin3\theta =sin(\frac{\pi }{2}-2\theta )$

$\Rightarrow 3\theta =\frac{\pi }{2}-2\theta$

$\Rightarrow 5\theta =\frac{\pi }{2}$

$\Rightarrow \theta =\frac{\pi }{10}$

$\therefore$ Statement 1 is true

Statement 2 is false,

One radian is the angle subtended at the circle by an arc of the same circle whose length is equal to the radius of that circle.

Only Statement 1 is true