Question

Which of the following is a true statement for 0 degrees less than theta less than 90 degrees?
a. tan theta = -tan theta
b. tan theta = tan (90 degrees - theta)
c. tan theta = -tan (180 degrees - theta)
d. none of the above

Answer 1

Answer:

c

Step-by-step explanation:

See the graph for an example using the specific angles $\theta=60^\circ , \,\, \180^\circ-\theta=120^\circ$

See how the red segments are equal  in length but going in opposite directions?

$\tan{60^\circ}=\sqrt{3} \\ \tan{120^\circ=-\sqrt{3}$

a. This can't be correct: it says $\tan{\theta}$ is equal to its opposite. That is never true in Quadrant I where all tangent values are positive.

b. Not true in Quad. I. Consider $\tan{60^\circ}, \,\, \tan{30^\circ}$.