# Question.

• Jan 27th 2010, 09:04 PM
Brndo4u
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.
• Jan 27th 2010, 09:09 PM
VonNemo19
Quote:

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.

$\displaystyle .6=\frac{6}{10}=\frac{3}{5}$ implies a 345 triangle

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

Can you see where I'm going?
• Jan 27th 2010, 09:36 PM
bigwave
since $\displaystyle cos\theta = \frac{3}{5}$ and $\displaystyle sin\theta = -\frac{4}{5}$

that means the hyp is 5 for both functions

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

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

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

hope this helps
• Jan 27th 2010, 09:40 PM
Prove It
Quote:

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:

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

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

If it equals $\displaystyle 1$ then there must exist some $\displaystyle \theta$ that holds for your conditions.
• Jan 27th 2010, 09:40 PM
Brndo4u
Yes.... thanks