Which point lies on the graph of y = tan x?

Which point lies on the graph of y = tan x?

• A. (0,0)
• B. (1,0)
• C. (0,1)
• D. (1,1)

Answer: (A)

The tangent function is sin x divided by cos x, so it equals zero exactly where sin x is zero (as long as cos x isn’t zero). At x = 0, sin 0 = 0 and cos 0 = 1, so tan 0 = 0. That makes the point (0,0) lie on the graph y = tan x. The other options don’t fit because they would require tan x to take the specified y-value at those x-values. For x = 0, tan 0 is 0, not 1, so (0,1) isn’t on the graph. For x = 1 (radians), tan 1 is about 1.557, not 0 or 1, so the points (1,0) and (1,1) aren’t on the graph either.

The tangent function is sin x divided by cos x, so it equals zero exactly where sin x is zero (as long as cos x isn’t zero). At x = 0, sin 0 = 0 and cos 0 = 1, so tan 0 = 0. That makes the point (0,0) lie on the graph y = tan x.

The other options don’t fit because they would require tan x to take the specified y-value at those x-values. For x = 0, tan 0 is 0, not 1, so (0,1) isn’t on the graph. For x = 1 (radians), tan 1 is about 1.557, not 0 or 1, so the points (1,0) and (1,1) aren’t on the graph either.