1. ## quick help with quadrants

i have a problem that is:

directions:
"Let theta be an angle in standard position. In which quadrant or quadrants can theta lie under the given conditions?"

Sin theta and tan theta have the same sign.

Can someone who answers this also explain how to do this problem? I have a unit circle graph but have no idea how to use it.... ty in advance

2. Originally Posted by d1338
i have a problem that is:

directions:
"Let theta be an angle in standard position. In which quadrant or quadrants can theta lie under the given conditions?"

Sin theta and tan theta have the same sign.

Can someone who answers this also explain how to do this problem? I have a unit circle graph but have no idea how to use it.... ty in advance
Hi d1338,

$tan\theta=\frac{sin\theta}{cos\theta}$

hence, an easy way to look at this is....

$sin\theta$ and $tan\theta$ have the same sign only when $cos\theta$ is positive.

Hence, you need to know where $cos\theta$ is positive, which occurs for angles to the right of the y-axis.

3. Originally Posted by d1338
i have a problem that is:

directions:
"Let theta be an angle in standard position. In which quadrant or quadrants can theta lie under the given conditions?"

Sin theta and tan theta have the same sign.

Can someone who answers this also explain how to do this problem? I have a unit circle graph but have no idea how to use it.... ty in advance
quad I ... sin and cos both (+)

quad II ... sin(+) , cos(-)

quad III ... sin and cos both (-)

note that tangent is the ratio of sine/cosine

4. Originally Posted by d1338
i have a problem that is:

directions:
"Let theta be an angle in standard position. In which quadrant or quadrants can theta lie under the given conditions?"

Sin theta and tan theta have the same sign.

Can someone who answers this also explain how to do this problem? I have a unit circle graph but have no idea how to use it.... ty in advance

This is how I learnt:
Remember ASTC : Add Sugar To Coffee

A: 1st quadrant: All identities are positive
S: 2nd quadrant: only sine is positive
T: 3rd quadrant: only tan is positive
C: 4th quadrant: only cosine is positive

5. All silver tea cups