The Unit Circle and Quadrants

What is the exact coordinates of  3π/4 on the unit circle?

• (−√2∕2, √2∕2)

• (−√2∕2, −√2∕2)

• (−√3∕2, −√2∕2)

• (√2∕2, −√2∕2)

What is 7π/4 radians in degrees?

• 300

• 135

• 315

• 45

sec 3π/2

• 0

• undefined

• 1

• -1

tan 7π/4

• -1

• 1

• √2/2

• undefined

Now, for Quadrant I of the Unit Circle, please complete the coordinates before we move onto finish Degrees to Radians. Recall the importance of Desmos. Recall the importance of thinking in terms of two number lines intersecting at, "(0, 0)."

b

a

c

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: tangent is positive: ​ (a)   ​& (b)   tangent is negative: ​ ​ (c)   &​ (d)   ​

• I

• III

• II

• IV

• Yes

• No

Answer explanation

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

True or False. All trig functions are positive in Quadrant IV.

• True

• False

sin 7π/6

• 1/2

• -1/2

• √3/2

• -√3/2