Find the value of the trigonometric function $\cos ec \left(-1410^{\circ}\right)$

The value of $2 \sin \left(12^{\circ}\right)-\sin \left(72^{\circ}\right)$ is

If $\sin \theta = \frac{{ - 4}}{5}$ and $\theta $ lies in the third quadrant, then $\cos \frac{\theta }{2} = $

Let the function $:(0, \pi) \rightarrow R$ be defined by

$f (\theta)=(\sin \theta+\cos \theta)^2+(\sin \theta-\cos \theta)^4$

Suppose the function $f$ has a local minimum at $\theta$ precisely when $\theta \in\left\{\lambda_1 \pi, \ldots, \lambda_{ T } \pi\right\}$, where $0<\lambda_1<\cdots<\lambda_r<1$. Then the value of $\lambda_1+\cdots+\lambda_r$ is. . . . . 

If $sin\theta_1 + sin\theta_2 + sin\theta_3 = 3,$ then $cos\theta_1 + cos\theta_2 + cos\theta_3=$

Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length.

$15\,cm$