Conversions/Sectors/Angular and linear speed
Right Triangle trigonometry
Law of Sines
Sum and Difference
Miscellaneous
100
Convert 5π/3 to Degrees.
Convert 5π/3 to Degrees. 5π/3(180º/π) 5•180º/3 900º/3 300º
100
What is the acronym that is used to remember the sin cos tan formulas?
SOH-CAH-TOA
100
A Triangle labeled Triangle ABC where B is 44º C is 53º A is 83º and side b=7 find side c.
b/sinB=c/sinC 7/sin44=c/sin53 sin53•7=5.59 5.59/sin44= 8.05 c=8.05
100
What are the pythagorean Identities?
sin2x+cos2x=1 1+cot2x=csc2x tan2x+1=sec2x
100
What does a generic tan graph look like?
://d2r5da613aq50s.cloudfront.net/wp-content/uploads/377254.image14.jpg
200
Convert -308º to Radians.
-308º(π/180º) -308•π/180 -154•π/90 -77π/45
200
A triangle has a 60º angle and adjacent to it is the side length is 5 what would the length of the side opposite of the 60 degrees be?
tan(60)=x/6 6•tan(60)=x x=5√3
200
Name an area formula for law of sines.
A=½absinC A=½bcsinA A=½acsinB
200
List three Reciprocal Identities.
sinx=1/cscx cscx=1/sinx cosx=1/secx secx=1/cosx tanx=1/cotx cotx=1/tanx tanx=sinx/cosx cotx=cosx/sinx Any Three of these are fine
200
Draw a unit circle.
http://www.softschools.com/math/trigonometry/images/unit_circle_charts_1.jpg
300
Find two angles one positive and one negative that are coterminal with 210º?
210+360= 570º 210-360=-150º 570º, -150º
300
A triangle has a 60º angle and adjacent to it is the side length is 5 what would the length of the side opposite of the 60 degrees be?
tan(60)=x/2√3 2√3•tan(60)=x x=6
300
Find the area of the triangle, given: angle B = 74.5º, a =103, c=58
A=½abSinB A= ½(103)(58)(sin74.5) A=½(103)(55.89) A=2878.36u2
300
find the exact value of the trigonometric function given that sin u=5/13 where π/2 ≤u≤π and where cos v=-3/5 where π/2 ≤u≤π.
tan(u + v) = sin(u + v) / cos(u + v) 12/3•3/5 + (5/12) -36/65•4/13 -72/130-40/130 112/130 56/65
300
What are coterminal angles?
Coterminal Angles are angles who share the same initial side and terminal sides.
400
A sector of a circle has a radius 6cm and a central angle of 0.5 radians. Find its a) arc length and b) area.
r=6 ø=.5 s=3 a). s=rø s=6•0.5 s=3 b). k=½(r)(s) k=½(6)(3) k=9
400
What is the exact side length of a square that has a diagonal length of twelve inches?
Label the right angle and the other two angles are 45º because its perfect square and the diagonal 12 inches. for an image. sin(45)=x/12 12•sin(45)=x x=6√2 inches
400
What is the ambiguous case?
In certain instances depending on angle sizes and side sizes, The law of sines does not work because the triangle is not possible, or the triangle has two two possible solutions.
400
find the exact value of the trigonometric function given sin(345º).
sin(345º) sin(300+45) sin300•cos45+cos300•sin45 (-√6+√2)/4
400
Where does a cosine graph start?
At the amplitude(negative if A is negative)
500
A wind machine used to generate electricity has blades that are 10 ft. in length. The propeller is rotating at 4 revolutions per second. Find the linear speed of the blade tips in ft/min.
v=rw v=(10)(8π) v=80π/sec• 60/1 min v= 4800π ft./ min
500
What isTraveling at a depth of 300 feet, a submarine dives at an angle of 20º with respect to a line parallel to the water’s surface. It travels a horizontal distance of 2000 feet during the dive. What is the depth of the submarine after the dive?
tan(20)+300=x/2000 2000•tan(20)+300=x 727.94+300=x x=1027.94 feet down
500
Find the area of the triangle, given: angle A= 50º, a =70, c=70
A=½cbSinA A= ½(70)(70)(sin50) A=½(490)(sin50) A=½(375.36) A=187.68u2
500
Find the exact value of cos(15).
cos(15) cos(45-30) cos45 •cos30 + sin45•sin30 (√2/2)(√3/2)+(√2/2)(1/2) √6/4+√2/4 (√6+√2)/4
500
Solve sinx+√2 =-sinx over the interval [0,2π].
sinx+√2 =-sinx +sinx +sinx 2sinx+√2=0 -√2 -√2 2sinx=-√2 /2 /2 sinx=-√2/2 5π/4, 7π/4
M
e
n
u