6.2 Answers

17-20

Number sin θ cos θ

tan θ csc θ sec θ cot θ

17 4/5 3/5 4/3 5/4 5/3 3/418 15/17 8/17 15/8 17/15 17/8 8/1519 12/13 5/13 12/5 13/12 13/5 5/1220 7/25 24/25 7/24 25/7 25/24 24/7

21-28

21. a=13.86, b=822. a=5, c=7.0723. b= 5.03, c=7.8324. a=27.47, c=29.2425. a=5.25, b=6.0426. a=1.04, b=3.8627. a=16.82, c=23.3828. a=21.10, c=32.86

33-38

33. 334. 1/535. 13/1236. 4/537. 24/738. 5/7

49-52

49. a= 12, b =12√3, c=12, d= 12 √350. a= (9 √3)/2, b= 4.5, c= 3 √3, d= (3 √3)/251. a=(14 √3)/3, b=(7 √3)/3, c= (14 √3)/3d= (14 √6)/352. a=15, b=15 √2, c=10 √6, d= 5 √6

6.4: Other Trigonometric Functions and Their Graphs

January 8, 2008

Objectives

• Learn definitions and basic trig identities• Represent other trig functions• Solve applications

Trig functions of any angle

x2+ y2 =r2

sin θ = y/rcos θ = x/rtan θ = y/x (when x ≠ 0)csc θ = r/y (when y ≠ 0)sec θ = r/x (when x ≠ 0)cot θ= x/y (when y ≠ 0)

Find the six trig functions

The point (15, -17) is located on the terminal side of an angle in standard position.

Reciprocal identities

sin θ = 1/csc θcos θ = 1/sec θtan θ = 1/cot θcsc θ = 1/sin θsec θ = 1/cos θcot θ = 1/tan θ

Find the six trig functions

sin θ = 9/41 cos θ = 40/41

Quotient identities

tan θ = sin θ/cos θcot θ = cos θ/sin θsin2θ + cos2θ=1

Find the six trig functions

sin θ =5/13 cos θ > 0

All about tangent

tan θ = y/xThis is the same thing as slope!Remember zero slope and undefined slope?Tan is zero and undefined at those same

values!

Graph of tangent

t -π/2 -π/3 -π/4 -π/6 0 π/6 π/4 π/3 π/2tan t und -√3 -1 -1/√3 0 1/√3 1 √3 und

Graph of cotangent

Graph of sine and cosecant

t -π -3π/4 -π/3 -π/4 0 π/4 π/2 3π/4 πcsc t und -√2 -1 -√2 und √2 1 √2 und

Graph of cosine and secant

Domain, range, period

Function Domain Range Period

sin t -∞<t<∞ -1 ≤sin t≤1 2πcos t -∞<t<∞ -1 ≤cos t≤1 2πtan t t≠ π/2 + πn -∞<tan t<∞ πcot t t≠ πn -∞<cot t<∞ πsec t t≠ π/2 + πn |sec t|≥1 2πcsc t t≠ πn |csc t|≥1 2π

This useful image is on p. 528

Assignment

1-18