Question

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

Answer 1

110°

Explanation:

You can use the phrase All Students Take Calculus to remember the signs of sin, cos, and tan.

110° falls in quadrant II, where only sin is positive and cos and tan are both negative.

Answer 2

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