write the function in terms of the cofunction of a complementary angle. \ncos\\frac{\\pi}{10}\n\ncos\\frac{\\…
write the function in terms of the cofunction of a complementary angle. \ncos\\frac{\\pi}{10}\n\ncos\\frac{\\pi}{10}=\\square (simplify your answer.)
Answer
Explanation:
Step1: Recall co - function identity
The co - function identity for cosine is (\cos\theta=\sin\left(\frac{\pi}{2}-\theta\right)).
Step2: Substitute (\theta = \frac{\pi}{10})
Substitute (\theta=\frac{\pi}{10}) into the co - function identity. We get (\cos\frac{\pi}{10}=\sin\left(\frac{\pi}{2}-\frac{\pi}{10}\right)).
Step3: Simplify the argument of the sine function
Calculate (\frac{\pi}{2}-\frac{\pi}{10}=\frac{5\pi - \pi}{10}=\frac{4\pi}{10}=\frac{2\pi}{5}).
Answer:
(\sin\frac{2\pi}{5})