6.2 Answers
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Transcript of 6.2 Answers
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