Question

Which angle has a tangent and cosine that are both negative? a. 110° b. 180° c. 210° d. 340°

Answer 1

110 degrees has tangent and cosine that are both negative

Solution:

We have to find the angle that has a tangent and cosine that are both negative

Option A)

$110^{\circ}$

$tan\ 110^{\circ} = -2.7474^{\circ}$

$cos\ 110^{\circ} = -0.3420^{\circ}$

Thus 110 degrees has tangent and cosine that are both negative

Option B)

$180^{\circ}\\tan\ 180^{\circ} = 0\\\\cos\ 180^{\circ} = -1$

Thus, 180 degrees does not have tangent and cosine that are both negative

Option C)

$210^{\circ}\\\\tan\ 210^{\circ}=0.5773^{\circ}\\\\\cos\ 210^{\circ} = -0.8660^{\circ}$

Thus, 210 degrees does not have tangent and cosine that are both negative

Option D)

$340^{\circ}\\\\tan\ 340^{\circ} = -0.3639\\\\cos\ 340^{\circ} = 0.9396$

Thus, 340 degrees does not have tangent and cosine that are both negative