One circle that draws every wave

Mathematics · Geometry · ages 16-17

Name ______________________ Date ____________

What is cos 60°?
Answer: ______________
What is sin 30°?
- 1
- 0
- 0.5
- -0.5
On the unit circle, what is sin 90 degrees?
- 0
- One half
- 1
On the unit circle, cosine is read off the y coordinate.
Circle one: True False
A sine wave peaks at 6 and troughs at -2. What is its amplitude?
Answer: ______________
In the second quadrant, cosine stays positive.
Circle one: True False
Use sin(180° − x) = sin x. What is sin 150°?
- -0.5
- 0.5
- 1
- 0
Maya says tangent has asymptotes where cosine is zero, at 90° and 270°. Is Maya right?
Circle one: True False
Where does y equals tan x break, and why?
- At 0 and 180 degrees, where sine is zero
- At 45 and 135 degrees, where values match
- At 90 and 270 degrees, where cosine is zero
What is sin 90°?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

0.5 · The 60° point has x coordinate one half.
0.5 · The 30° circle point has height one half. The 1 option is sin 90°.
1 · At 90 degrees the point is (0, 1), and sine reads the y coordinate.
False · Cosine reads x while sine reads y.
4 · Range 8, half of that is 4.
False · Past 90 degrees x turns negative while y stays positive.
0.5 · sin 150° = sin 30° = 0.5. The −0.5 option misses the mirror keeping height positive.
True · Division by zero breaks tan there.
At 90 and 270 degrees, where cosine is zero · Tangent divides by cosine, and division by zero has no value.
1 · Top of the circle has height 1.