Answer: a) [tex]\frac{1}{2}[/tex]
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 [tex]2\pi\ or\ 360^{\circ}[/tex]
∴ [tex]\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}[/tex]
[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 [tex]\pi\ or\ 180^{\circ}[/tex]
∴ [tex]\tan\frac{13\pi}{4}=\tan(3\pi+\frac{\pi}{4})=\tan{\frac{\pi}{4}}=1[/tex]
(c) sec 11π/3
[tex]\text{Since, }\sec(x)=\frac{1}{\cos x}[/tex]
[tex]\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[/tex]
