January 20th BOOK 4.2 copyright2009merrydavidson

All Students Take Classes

Determine in which quadrant each trig function is positive.

QI: AllQII: sin/csc

QIII: tan/cot QIV: cos/sec

Trig Identities

f(x) = cos x f(x) = sin x

EVEN ODD

sin sinx x csc cscx x

cos cosx x sec secx x

Trig Identities

f(x) = tan x

ODD

tan tanx x

cot cotx x

Practice…

Follow the correct order of operations.

1. Find sin 180 (a quandrantal angle)

2. Find 3 cot 7/6

3. Find tan 120 + cot (-30)

4. csc /2 sin /2

3 3

0

3(cos/sin) =

3 3 2 3

1

Practice…

5) If cos (-t) = -1/5,

a) find cos (t) b) find sec (-t)

-1/5 -5

Given 1 trig function, find the value of the remaining 5.

6) sin (t) = ¼, find the remaining values.

Step 1: ¼ is positive so draw a right triangle in quadrant I because sine is positive in quadrant 1.

Step 2: Label opposite and hypotenuse.

14

Step 3: Use pythagorean Thm. To find the missing side.

15

Step 4: Use sohcahtoa to

find the missing trig values. Be sure to rationalize the denominator when necessary.

t

sin t = csc t =

cos t = sec t =

tan t = cot t = 15

154 15

15

41/ 4

15

4

4 15

15

Given 1 trig function, find the value of the remaining 5.

7) tan (t) = 2/5; find the remaining values.

Step 1: 2/5 is positive so draw a right triangle in quadrant I because tangent in positive in QI.

Step 2: Label opposite and adjacent.

2

5

Step 3: Use pythagorean Thm. To find the missing side.

29Step 4: Use sohcahtoa to

find the missing trig values.t

sin t = csc t =

cos t = sec t =

tan t = cot t =

2 29

29

29

2

5 / 22 / 5

5 29

29

29

5

EX 8: The terminal side of an angle with measure in standard position passes through (4,-5). Sketch the

reference angle. Evaluate sin , cos , and cot .

41(4,-5)

Step 1: draw what you know.

-5

4

Step 2: Find the hypotenuse.

Step 3: Use SOHCAHTOA to find what is asked.

sin = -5 / 41

cos = 4 /41 cot = -4/5

41

41

EX 9: Terminal side of an angle with measure , in standard position, ending at (-4,7).

Evaluate all six trig functions.

EX 10: is given in standard position in QII and sin = 2/7, find cos , tan , and sec .

In QII the x value is NEGATIVE

EX 11: is in standard position in quadrant III, and tan = 2/5. Find sin , csc and cot .

In QIII the x value and

y value’s are NEGATIVE!

The radius is ALWAYS positive.

Quiz Monday over:

• Fill in a blank unit circle with everything.• Give the (x,y) ordered pairs for specific radian values.• Give the sine/cosine at certain radian values.• Given a specific trig value, find the other 5 trig values.• Given a point on the terminal side of an angle, find the 6

trig functions.• Know which trig functions are even and odd.• Know the period for all 6 trig functions.• Given a right triangle, find 2 of the sides and/or 2 of the

angles using SOHCAHTOA.• Answer 2 application problems using SOHCAHTOA.

HW: WS 6-6

study for quiz