Sine and Cosine with Radians

What will a person on this Ferris wheel be doing 67 seconds into their ride?

• Increasing at an increasing rate.

• Increasing at a decreasing rate.

• Decreasing at a decreasing rate.

• Decreasing at an increasing rate.

Answer explanation

Every 8 seconds is a cycle. So, at 64 seconds, the Ferris wheel starts a new cycle. The rider reaches their highest at 68 seconds. So, at 67 seconds, the graph is increasing and concave down (decreasing rate).

Which angle in radians best matches the drawing in standard position?

• π/2

• π/3

• π/4

• π/6

Answer explanation

Which angle in radians best matches the drawing in standard position?

• 5π/6

• 5π/3

• 10π/6

• 11π/6

Answer explanation

Which angle in radians best matches the drawing in standard position?

• 5π/3

• 7π/4

• 4π/3

• 5π/6

Answer explanation

Find the exact value of the following trig expressions.

• 0

• 1

• -1

Answer explanation

At 100 seconds into the ride, will the rider be at the highest point (rel. max), lowest point (relative min), or neither?

• Highest

• Lowest

• Neither

Answer explanation

At 96 seconds (divisible by 8), a new cycle starts. Four seconds later, the rider is at their highest.

Unlike right triangle trigonometry, sine and cosine may be negative. Thinking about how sine, cosine, and tangent relate to (x,y) coordinate pairs on the unit circle, find the quadrants where: sine is positive: ​ (a)   ​& (b)   sine is negative: ​ ​ (c)   &​ (d)  

• I

• II

• III

• IV

Answer explanation

What matching best completes Quadrant II of the Unit Circle with Radian Measures?

• a

• 
• c

• 
• b

• 

Answer explanation

What matching best completes Quadrant VI of the Unit Circle with Radian Measures?

• b

• 
• a

• 
• c

• 

Answer explanation

.

A periodic function get their name because they:

• Have behavior that repeats infinitely

• They are punctuation functions

• Are finite in nature

• They attract bears