CPM Homework Help : PC Problem 6-74

Christina stared at the equation tan x = . “That’s interesting,” she thought. “Since tan x = , this must mean that sin x = 3 and cos x = 7. But that’s impossible.” Homework Help ✎
1. Why is it impossible?
2. What’s going on here?
3. Find x if 0 ≤ x ≤ 2π.

Hint (a):

What is the range of sine and cosine?

Answer (b):

$\text{For example, }\frac{0.3}{0.7}=\frac{3}{7}.$

Hint (c):

$\text{Using a calculator evaluate }\tan^{-1}\left (\frac{3}{7} \right ).$

More Help (c):

There is another solution. Use the unit circle to help you calculate the second solution.