chapter 9
*MAKE SURE ALL INVERSES ARE IN RADIANS* answer: π/3 remember that sine is the y and the y coordinate that is (√3/2) falls under 60 degrees which is π/3
find sin-1(√3/2)
multiply by π/180 EX: 220 to degrees is (220/1)(π/180) would equal 220π/180 which simplifies to 22π/18 to....... 11π/9
how do you convert from degrees to radians
multiply by 180/π EX: 5π/8 to get to radians (5π/8)(180/π) which equals 900π/8π which simplifies to.... 112.5
how do you convert from radians to degrees
FIRST TURN ϴ INTO RADIANS EQ: A=(1/2)ϴr^2 EX: {given: ϴ=170 and r=20} you would turn ϴ into radians by (170/1)(π/180) which would give you 17π/18 then you would use the equation to multiply by (1/2) which would get you 1.48 then multiply by r^2 which would be 20^2 to get you 593.41
how do you find area of a sector
TURN THETA INTO RADIANS then multiply by the radius EQ: S=ϴr EX: {given: ϴ=170 and r=20} you would use the equation S=ϴr so first turn theta into radians, to do that you would (170/1)(π/180) which would give you 17π/18, that is now theta, then multiply by r which is 20 (17π/18)(20) to get you 59.34
how do you find the arc length
first you find S, the equation is S=perimeter/2, then you plug 's' into the area equation which is → A=√S(s-a)(s-b)(s-c)
how do you find the area of a triangle
square both side lengths then SQUARE ROOT THE ANSWER EX: if short side is 5 and long side is 12 then you would use the equation a^2 + b^2 = c^2 so 5^2 + 12^2 is 169 so you would square root that to get 13
how do you find the hypotenuse
first you need to find out the quadrant it is in, in this case 210 is between 180 and 270 so it is in Q3, now find the nearest x axis angle in this case it is 180, now you do 210-180 to get the reference angle which is 30°
how do you find the reference angle of 210°
first you need to find a coterminal angle because it is over 2π so you do (24π/7)-(14π/7) which would give you the co terminal angle of 10π/7 now you find out what quadrant it is in in this case it is in Q3, now you have to find the nearest x axis which is π so you do 10π/7 - 7π/7 to give you the reference angle of 3π/7
how do you find the reference angle of 24π/7
ASA, law of sine
if A, b, C was given what type of triangle would it be and what law would you use
AAS, law of sine
if A,C, a was given what type of triangle would this be and what law would you use
SSS law of cosine
if a, b, c was given what type of triangle would this be and what law would you use
NEVER USE LAW OF SINE TO FIND THE BIGGEST ANGLE SAS, law of cosine SOLVE: solve for b first, b^2=a^2+c^2-2acCOSB → b^2=196+2209-1316(0.87) → b^2=2405-1151 → b^2=1254 → b=35.41 Now we have a repeat letter so we can use law of sines to find the rest
if a=14, B=29°, c=47 how would you solve the equation
NEVER USE LAW OF SINE TO FIND BIGGEST ANGLE SSS, law of cosine SOLVE: *SOLVE FOR BIGGEST ANGLE FIRST* biggest anlge is across from biggest side so it is angle a and now plug into the equation by using the law of cos equation { a^2=c^2+b^2-2(c)(b)COS(A) } so 23^2=(13^2+18^2)-2(13)(18)COSA → 529=(169+324)-468COSA → 529=(493)-468COSA → 36=-468COSA → -(1/13)=COSA → COS-1-(1/13)=A so A is 94.4 then use law of sines to find the rest
if a=23, b=18, c=13 how would you solve the triangle
SAS, law of cosine
if b, C, a was given what type of triangle would this be and what law would you use
first remember the equations → S=perimeter/2 and A=√S(s-a)(s-b)(s-c) → S=18/2 → S=9 → A=√9(4)(3)(2) → √216 → A=14.7
if those are the side measurements of a triangle, find the area
SAS or SSS
what do you use for law of cosines
c^2=a^2+b^2-2(a)(b)COS(C)
what is the law of cosine equation
AAS or ASA
when do you use law of sines