Identifying Trig Graphs worksheet - Free Printable

Let’s go step by step to label the graphs in Section A and understand what each trigonometric function looks like.

---

Step 1: Recall basic shapes of sin, cos, tan

- y = sin x: Starts at (0,0), goes up to max at 90°, back to 0 at 180°, down to min at 270°, back to 0 at 360°.
- y = cos x: Starts at (0,1), goes down to 0 at 90°, min at 180°, back to 0 at 270°, max at 360°.
- y = tan x: Has vertical asymptotes at 90° and 270° (where it shoots up or down to infinity). Passes through (0,0), (180,0), (360,0). Between 0°–90° it goes from 0 to +∞; between 90°–180° it comes from -∞ to 0; etc.

---

Step 2: Match first graph (top left)

Graph starts at (0,0), peaks at 90°, crosses zero at 180°, trough at 270°, back to zero at 360° → This is sin x.

✔ So top left: y = sin x

---

Step 3: Match second graph (top right)

Starts at (0,1), goes down to 0 at 90°, lowest at 180°, back to 0 at 270°, highest again at 360° → This is cos x.

✔ Top right: y = cos x

---

Step 4: Match third graph (bottom middle)

Has breaks/asymptotes at 90° and 270°. Goes from 0 up to +∞ before 90°, then from -∞ up to 0 after 90°, same pattern repeats. That’s classic tangent behavior.

✔ Bottom middle: y = tan x

---

Now for Section B — we are asked to sketch the graphs. Since this is text-based, I’ll describe how to draw them accurately on the given grids.

But note: The user only uploaded the worksheet — they didn’t ask us to *draw* anything physically. However, since Section B says “Sketch the graphs”, and we’re solving the problem, we should provide guidance on how to sketch them correctly based on standard knowledge.

Wait — actually, looking again: In Section A, we are to LABEL the graphs with correct functions. In Section B, we are to SKETCH the graphs of given functions. But since we can't draw here, perhaps the expectation is just to know what they look like? Or maybe the student will draw them themselves?

Actually — re-reading the instructions: The user said “Solve the problem accurately.” And the problem has two sections:

- Section A: Label each graph → We did that.
- Section B: Sketch the graphs → We can’t sketch visually, but we can describe exactly how to do it so the student can draw it.

But wait — let me check if there's any trick. Looking at Section B:

There are four blank grids:

1. y = cos x → grid from 0 to 360, y from -1 to 1
2. y = tan x → grid from 0 to 360, y from -3 to 3
3. y = sin x → grid from 0 to 360, y from -1 to 1
4. y = cos x → grid from -360 to 360, y from -1 to 1 ← this one includes negative angles!

So for Section B, we need to tell the student how to sketch each.

But hold on — the original instruction says: “Do not describe the image.” Also, “CRITICAL: First work through the problem step by step... ONLY THEN provide the final answer.”

And the Final Answer section should contain only the final correct answer.

What is the “final correct answer” for this task?

In Section A, we have three blanks to fill:

Top left: y = ___
Top right: y = ___
Bottom middle: y = ___

We determined:

→ Top left: sin x
→ Top right: cos x
→ Bottom middle: tan x

For Section B, since it’s “sketch”, and we can’t produce images, perhaps the expected output is just the labels for Section A? Because Section B requires drawing, which isn’t possible in text.

Alternatively, maybe the problem expects us to recognize that Section B is practice for the student to do themselves, and our job is only to solve Section A?

Looking at the structure: The page says “FOLD THE PAGE SO THAT YOU CANNOT SEE THE ANSWERS ABOVE” — meaning Section A answers are meant to be hidden when doing Section B. So likely, the main solvable part is Section A.

Also, in many such worksheets, Section A is matching/labeling, Section B is application (drawing). Since we’re an assistant helping solve homework, and we can’t draw, we should focus on providing the correct labels for Section A.

Moreover, the user options are all false — no explanation, no teaching, no practice — so we just give the final answer.

Thus, the final answer should be the three function names for the three graphs in Section A.

Let me double-check:

First graph (starts at origin, sine wave): sin x ✔️
Second graph (starts at peak, cosine wave): cos x ✔️
Third graph (asymptotes at 90, 270): tan x ✔️

Yes.

Final Answer:
y = sin x
y = cos x
y = tan x