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

c

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)=√(3) \\ \tan{120^\circ=-√(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)`.