Question

Find the exact value of each of the following. In each case, show your work and explain the steps you take to find the value.
(a) sin 17π/6
(b) tan 13π/4
(c) sec 11π/3

Answer 1

Answer: a) $\frac{1}{2}$

b) 1

c) 2

Step-by-step explanation:

(a) sin 17π/6  

It is known that the value of sin x repeat after an interval of $2\pi\ or\ 360^{\circ}$

∴ $\sin\frac{17\pi}{6}=\sin2\frac{5\pi}{6}=\sin(2\pi+\frac{5}{6}\pi)=\sin{\frac{5}{6}\pi}=\sin(\pi-\frac{\pi}{6})=\sin(\frac{\pi}{6})=\frac{1}{2}$

[Since the value of sin x is positive in 2nd quadrant]

(b) tan 13π/4  

It is known that the value of sin x repeat after an interval of $\pi\ or\ 180^{\circ}$

∴ $\tan\frac{13\pi}{4}=\tan(3\pi+\frac{\pi}{4})=\tan{\frac{\pi}{4}}=1$

(c) sec 11π/3

$\text{Since, }\sec(x)=\frac{1}{\cos x}$

$\cos(\frac{11\pi}{3})=cos(\frac{5\pi}{3}+2\pi)=\cos(\frac{5\pi}{3})=\cos(6\pi-\frac{\pi}{3})=\cos(\frac{\pi}{3})=\frac{1}{2}\\\Rightarrow\sec(\frac{11\pi}{3})=\frac{1}{\cos(\frac{11\pi}{3})}=2$