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Jobisdone [24]
3 years ago
12

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.

Mathematics
1 answer:
mote1985 [20]3 years ago
4 0

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

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