1. ## Question.

The question is, Does there exist an angle theta with the function values COS theta=.6 and SIN theta=-.8.....could someone explain this to me. Not really sure what is meant by the question.

2. Originally Posted by Brndo4u
The question is, Does there exist an angle theta with the function values COS theta=.6 and SIN theta=-.8.....could someone explain this to me. Not really sure what is meant by the question.
$.6=\frac{6}{10}=\frac{3}{5}$ implies a 345 triangle

$.8=\frac{8}{10}=\frac{4}{5}$ implies a 345 triangle

Can you see where I'm going?

3. since $cos\theta = \frac{3}{5}$ and $sin\theta = -\frac{4}{5}$

that means the hyp is 5 for both functions

since $cos\theta$ is postive it must be in Q-I or Q-4

since $sin\theta$ is negative it must be in Q-3 or Q-4

so $\theta$ exists and is in Q-4

hope this helps

4. Originally Posted by Brndo4u
The question is, Does there exist an angle theta with the function values COS theta=.6 and SIN theta=-.8.....could someone explain this to me. Not really sure what is meant by the question.
From the Pythagorean Identity:

$\cos^2{\theta} + \sin^2{\theta} = 1$.

So check what $(0.6)^2 + (-0.8)^2$ equals.

If it equals $1$ then there must exist some $\theta$ that holds for your conditions.

5. Yes.... thanks