Question.

**Brndo4u** · January 27th 2010, 09:04 PM

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.

**VonNemo19** · January 27th 2010, 09:09 PM

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?

**bigwave** · January 27th 2010, 09:36 PM

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

**Prove It** · January 27th 2010, 09:40 PM

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.

**Brndo4u** · January 27th 2010, 09:40 PM

Yes.... thanks

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