Question

find tan theta if cos theta = 1/4 and sin theta < 0

use the fundamental identities to find the value of the trigonometric function

Answer 1

For solving this do you know the conception of : Trigonometric Functions.

Answer 2

YES
can you actually help me get the answer tho?

Answer 3

ok leave that. tell me, how do you relate sec theta with cos theta?

Answer 4

sec theta = 1/cos theta

Answer 5

yes. so sec theta = 1/1/4 = 4.

Now which identity relates sec theta with tan theta?>

Answer 6

1 + tan^2 theta = sec^2 theta

Answer 7

yes.

So 1 + Tan^2 theta = 4^2

Tan^2 theta = 15.

Hence Tan theta = sqrt(15).

You never needed sin for that! :P

Answer 8

if \(sin(\theta) <0\) meaning negative, \(tan(\theta)\) will also be negative

Answer 9

meaning either III or IV quadrant

Answer 10

ok that totally helped me understand, but for some reason the answer options are