Unit 9 - The Unit Circle

Family

100

Name the family members of the 30 degree family

30, 150, 210, 330

200

Name the family members of the pi/4 family

pi/4, 3pi/4, 5pi/4, 7pi/4

300

Name the family members for the pi/10 family.

pi/10, 9pi/10, 11pi/10, 19pi/10

400

Name the family members of the family whose cosine value is +/- rt(3)/2 (in RADIANS).

pi/6, 5pi/6, 7pi/6, 11pi/6

500

Name the family members of the family whose cotangent value is +/- 1/rt(3)

pi/3, 2pi/3, 4pi/3, 5pi/3

Trig Values

100

sin(17pi/4)

1/rt2

200

sec(pi/3)

2

300

sin(11pi/3)cos(-3pi/4)tan(7pi/4)

-rt(3)/(2rt2)

400

cos(21pi)csc(21pi/4)sec(22pi/3)

-2rt2

500

cos(7pi/4)sec(17pi/6) + sin(19pi/2)tan(13pi/4)

-2/rt6 - 1

Trig Equations

100

cosx + rt3 = -cosx, 0<x<2pi

5pi/6, 7pi/6

200

4sin²x-3=0, 0<x<2pi

pi/3, 2pi/3, 4pi/3, 5pi/3

300

2sin²x-3sinx+1=0

pi/6, 5pi/6, pi/2

400

2cosxsinx=cosx, 0<x<2pi

pi/6, 5pi/6, pi/2, 3pi/2

500

secxcscx + rt2cscx = 0

3pi/4, 5pi/4

Quadrants

100

In which quadrant(s) is tangent positive?

I, III

200

In which quadrant(s) is sine negative and cosine positive?

IV

300

In which quadrants is secant positive and tangent negative?

IV

400

In which quadrant(s) is tangent positive and cotangent negative?

None!

500

In which quadrant(s) is cosecant negative and tangent positive?

III

Trig Functions

100

If sinx = 3/5 and cosx<0, determine tanx.

-3/4

200

If cosx=1/3 and tanx<0, determine sinx.

-2rt/3

300

If tanx=3/5 and secx<0, determine cosx.

-5/rt(34)

400

If cscx=5 and tanx<0, determine cosx.

-2rt6/5

500

If secx=-3 and sinx<0, determine tanx.

2rt2