Exercícios 6.5 Exercícios
1.
Dada a medida do ângulo em graus, determine a medida correspondente em radianos.
- \(\displaystyle 45º\)
- \(\displaystyle -60º\)
- \(\displaystyle 30º\)
- \(\displaystyle 345º\)
- \(\displaystyle -300º\)
- \(\displaystyle 175º\)
2.
Determine o valor exato de cada expressão.
- \(\displaystyle \sin\dfrac{2\pi}{3}\)
- \(\displaystyle \cos\dfrac{2\pi}{3}\)
- \(\displaystyle \tan\dfrac{2\pi}{3}\)
- \(\displaystyle \sin\dfrac{7\pi}{6}\)
- \(\displaystyle \cos\dfrac{7\pi}{6}\)
- \(\displaystyle \sec\dfrac{7\pi}{6}\)
- \(\displaystyle \mbox{cossec}\dfrac{7\pi}{6}\)
- \(\displaystyle \mbox{cotg}\dfrac{7\pi}{6}\)
- \(\displaystyle \tan \dfrac{11\pi}{6}\)
- \(\displaystyle \sec \dfrac{11\pi}{6}\)
- \(\displaystyle \mbox{cossec}\dfrac{11\pi}{6}\)
- \(\displaystyle \mbox{cotg}\dfrac{11\pi}{6}\)
3.
Se \(\cos\theta=-\dfrac{4}{5}\) e \(\pi\leq \theta\leq \dfrac{3\pi}{2}\text{,}\) determine:
- \(\displaystyle \sin\theta\)
- \(\displaystyle \sec\theta\)
- \(\displaystyle \mbox{tg}\hspace{0.05cm}\theta\)
- \(\displaystyle \mbox{cossec}\hspace{0.05cm}\theta\)
- \(\displaystyle \mbox{cotg}\hspace{0.05cm}\theta\)
4.
Considerando que as funções trigonométricas são periódicas - isto é, \(f(t)=f(t+2\pi k)\text{,}\) em que \(k\) é um inteiro - determine o valor de:
- \(\displaystyle \sin\dfrac{43\pi}{4}\)
- \(\displaystyle \cos\dfrac{31\pi}{6}\)
- \(\displaystyle \mbox{tg}\hspace{0.05cm}\left(\dfrac{-22\pi}{3}\right)\)
- \(\displaystyle \mbox{cotg}\hspace{0.05cm}\left(\dfrac{-31\pi}{4}\right)\)
- \(\displaystyle \sec\dfrac{71\pi}{6}\)
- \(\displaystyle \mbox{cotg}\hspace{0.05cm}\left(\dfrac{-91\pi}{3}\right)\)
5.
Considerando \(\dfrac{5\pi}{6}+\dfrac{\pi}{4}=\dfrac{13\pi}{12}\text{,}\) determine:
- \(\displaystyle \sin\dfrac{13\pi}{12}\)
- \(\displaystyle \cos\dfrac{13\pi}{12}\)
- \(\displaystyle \mbox{tg}\hspace{0.05cm}\dfrac{13\pi}{12}\)
6.
Determine o valor exato de cada expressão, se estiver definido.
- \(\displaystyle \arcsin\dfrac{1}{2}\)
- \(\displaystyle \arccos\left(-\dfrac{\sqrt{3}}{2}\right)\)
- \(\displaystyle \arctan(-1)\)
- \(\displaystyle \arcsin\left(-\dfrac{\sqrt{3}}{2}\right)\)
- \(\displaystyle \arccos\left(-\dfrac{\sqrt{2}}{2}\right)\)
- \(\displaystyle \arctan(-\sqrt{3})\)
- \(\displaystyle \arcsin\left(-\dfrac{1}{2}\right)\)
- \(\displaystyle \arccos\dfrac{1}{2}\)
- \(\displaystyle \arctan\left(\dfrac{\sqrt{3}}{3}\right)\)
- \(\displaystyle \arcsin(-1)\)
- \(\displaystyle \arccos 1\)
- \(\displaystyle \arctan 0\)