cos 360 + cos 234 + cos 162 + cos 18 = ? Note - numbers are in degree.

If ${\displaystyle \sin x+\sin y=a\text{and}\cos x+\cos y=b}$ then find ${\displaystyle \tan (x-\frac{y}{2})}$

Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 11 passengers per minute.

Find derivative of trigonometric function ${\displaystyle y=\frac{3(1-\sin x)}{2\cos x}}$

Which statement cannot be true? Explain.
A. ${\displaystyle \sin A=0.5}$
B. ${\displaystyle \sin A=1.2654}$
C. ${\displaystyle \sin A=0.9962}$
D. $\sin A=\frac{3}{4}$

Trigonometric Identify: $\frac{1+\cos x}{\sin x}=\cot \frac{x}{2}$

if $x=2,f(x)=1$
if $x=3,f(x)=4$
if $x=5,f(x)=-2$
if $x=8,f(x)=3$
if $x=13,f(x)=6$
f is twice variable for all real numbers.
1. Find $f^{\prime }(4)$
2. Approximate ${\displaystyle {\underset{2}{\int }}^{13}{f}^{\prime }\left(x\right)dx}$
2. Find the value of ${\displaystyle {\underset{2}{\int }}^8(3-f^{\prime }\left(x\right))dx}$

Is there an inequality for $\sinh (x)$ which is similar to this inequality $\cosh (x)\le e^{x^2/2}$