math

TRIANGLE Solve the triangle shown to the right a = 11 b = 8 c = 8

(Use the formula a^2 = b^2 + c^2 - 2bc cosA) cosA = 8^2 + 8^2 - 11^2 / 2(8)(8) = 7/128 Next do the cos^-1(7/128) A = 86.9° sinC = 8sin86.9/11 C = 46.6° (inverse jawn) B = 46.6° (SAME AS C)

TRIANGLE A triangular truss is shown in the figure. Find the angle theta 11ft 11ft 9ft

9^2 = 11^2 + 11^2 - 2(11)(11)costheta costheta = 8^2 + 8^2 - 5^2 / 2(8)(8) = 0.8047 cos^-1(0.8047) = 36°

TRIANGLE A ship is sailing east. At one point, the bearing of a submerged rock is 43° 20'. After the ship has sailed 17.2 mi, the bearing of the rock has become 306° 40'. Find the distance from the rock at the latter point. 17.2 mi

A = 90° - 43° 20' = [A = 46° 40'] B = 306° 40' - 270° = [B = 36° 40'] C = 180 - 46° 40' - 36° 40' = (178° 120' - 46° 40' - 36° 40') = [C = 96° 40'] a = 17.2sin46°40'/sin96°40' a= 12.6

Solve the equation on the interval [0 , 2pi), then support your solutions graphically cos2x - cosx = 0

First change cos2x to 2cos^2x - 1 2cos^2x - 1 cosx -1 Set = to 0, and move jawns over to right side cosx = 1 and cosx = -1/2 Then find the solution set with unit circle {2pi/3 , 4pi/3, 0}

Solve the equation for exact solutions over the interval [0, 360°) sin(2theta)=1

First find that sin(1) = 90° Next set it up with "n" 2theta = 90 + 360n Next divide 2 on the shits theta = 45 + 180n Then set n = 0 and also = 1 45 + 180(0) = 45° and 45 + 180(1) = 225° {45° , 225°}

Solve the equation for solutions in the interval [0,2pi). Use algebraic methods and give exact values. Support your solution graphically. cos2x = sqrt(2)/2

First find the jawn on the unit circle pi/4, 7pi/4 , 9pi/4, and 15pi/4 Next multiply the denominators by 2 {pi/8, 7pi/8, 9pi/8, and 15pi/8}

Solve the equation for solutions over the interval [0,2pi) by first solving for the trigonometric function (sec x - 2)(sqrt3) secx + 2) = 0

First set both parenthesis jawns = to 0 secx-2=0 and sqrt3)secx+2 =0 Next add the jawns onto the other side secx =2 and sqrt(3)secx = -2 (÷sqrt(3) to get -2/sqrt3) Next, Use the unit circle to find the amounts secx = 2 = cos(1/2) = {pi/3 , 5pi/3} secx = -2/sqrt(3) = reciprocal -sqrt(3)/2 = {5pi/6 , 7pi/6}

A = 44.7° a = 8.3m b = 10.5m

sinB = 10.5sin44.7°/8.3 = 62.9°

Solve the triangle, if possible. Determine the number of possible solutions. A = 36.5° a = 3.8 c = 17.2

sinC = 17.2sin36.5° / 3.8 sinC = 2.7 But there is no sin value whose value is greater than 1 so there is no solution.

TRIANGLE Find the horizontal component, a, of vector u. 17 , 45°

Just find the sin of 45° (which is sqrt(2)/2) and then at the 17 infront of it 17sqrt(2)/2

Write the vector u = (5, -10) in i, j form

Just put an i after 5 and j after 10 5i - 10j

TRIANGLE Find the magnitude of the vector u. u = (1 , - sqrt(3))

sqrt(5sqrt(3)^2 + 5^2) = sqrt100 = 10

Find the area of the triangle ABC C = 132.2°, a = 46.4 ft and b = 37.9 ft

(USE FORMULA: Area = 1/2ab sin(C°) First substitute the values into the formula Area = 1/2(46.4)(37.9)sin(132.3)° = 650.3 (rounded to the nearest tenth)

Find the magnitude and positive direction angle of the vector (-5, -5sqrt(3))

Find the magnitude which is sqrt(-5^2+-5sqrt3^2) = sqrt(100) = 10 Find the direction angle by using tan -5sqrt(3)/-5 = sqrt(3) [the 5's cancel out] tan^-1(sqrt(3) = 60° add 180° + 60° = 240°

Solve the equation for solutions over the interval [0,2pi) by first solving for the trigonometric function 6sinx+15=12

First subtract 15 onto 12 6sinx = -3 Next divide 6 onto -3 sinx = -1/2 Finally, Use the unit circle to find the values for the jawn {11pi/6 , 7pi/6}

Find the exact value of the real number y if it exists (6.1.33) y=sec^-1(-2)

Put a 1 over that jawn since it is the reciprocal of the shit = cos^-1(-1/2) Use the calculator to find it equals 120° Use the unit circle to find that 120° = 2pi/3

Give the degree measure of theta if it exists. theta = arcsin(1/2)

Put the jawn in the calculator as sin^-1(1/2) You will get 30° as the answer

Use an appropriate area formula to find the area of the triangle with the given side lengths. a = 14m b = 9m c = 10m

S = 14 + 9 + 10 / 2 = [S = 16.5] Area = sqrt(16.5(16.5 - 14)(16.5 - 9)(16.5 - 10)) = sqrt(2010.9375) area = 44.8

TRIANGLE Solve the triangle A = 36° b = 15 c = 29

Solve for a a^2 = 15^2 + 29^2 - 2(15)(29)cos36° = 362.16 Next square root that answer a = sqrt(362.16) = 19 Next solve for cosB 15^2 = 19^2 + 29^2 - 2(19)(29)cosB -977 = -1102cosB (combine 15^2 - 19^2 -29^2 so it is -977) Next inverse the result of -977/-1102 = 0.88657 = B = 28° To find angle C you subtract 180 by 28° and 36° 180° - 36° - 28° = 116° A = 36° a = 19 B = 28° b = 15 C = 116° c = 29

Find the exact value of the real number y if it exists (6.1.17) y=tan^-1(-sqrt3)

Use the calculator to find the degree = -60° Use the unit circle to find -60° = -pi/3

Find the exact value of the real number y if it exists (6.1.13) y=sin^-1(-sqrt3/2)

Use the calculator to find the degree = 60° Use the unit circle to find 60° = pi/3 since it is negative sqrt3/2 it is gonna equal -pi/3

Solve the triangle ABC, if the triangle exists. A = 44.7° a = 8.3 b = 10.5

sinB = 10.5sin44.7° / 8.3 = 0.88984 (inverse that) B1 = 62.9° B2 = 180° - 62.9° = 117.1° To find C1 you do 44.7° + 62.9° - 180° C1 = 72.4° C2 = 180° - 62.9° - 44.7° = 18.2° Find c1 c1 = 8.3sin72.4°/sin44.7° = 11.2 c2 = 8.3sin18.2°/sin44.7° = 3.7

Find the magnitude and the positive direction angle for u. u = (20, -21) (Find |u| and theta)

|u| = sqrt(20^2 + -21^2) sqrt(400 + 441) sqrt(841) = 29 ____ To find theta use tantheta = -21/20 (inverse) = -46.4° Theta = -46.4° + 360° = 313.6°

Solve the equation for solutions over the interval [0°,360°) 10tan^2theta costheta -5 tan^2 theta = 0

First factor it so... 5tan^2theta(2 costheta -1) =0 Next set both parenthis jawns equal to 0 5tan^2 theta = 0 and 2 costheta -1 = 0 Then get the shits over tantheta = 0 and costheta = 1/2 Finally make the jawns to equal to degrees {0° , 60° , 180° , 300°} [ANSWER] (360-60 = 300) (0+180 = 180)

Give the exact value of the expression (6.1.75) tan(arcsin(-1/2))

First solve in calculator sin^-1(-1/2) = -30° Second use unit circle to find tan(-30) = -sqrt3/3 *Don't forget tan is sin/cos or y/x : (x,y)

Give the exact value of the expression (6.1.79) sin(2tan^-1 (-15/8))

First square root the lengths that are squared so... sqrt(8)^2 + (-15)^2 = sqrt(64 + 225) = sqrt(289) = 17 Next plug in 17 as the denominator for the jawns sinA = (-15/17) cosA = (8/17) Then multiply those jawns by 2 2(-15/17)(8/17) = -240/289 Thats your answer -240/289

TRIANGLE Find the length of side a A<60° B<75° c = 6sqrt(2)

First subtract 180 by 75 and 60 45° Next solve for a so... a = 6sqrt(2)sin60° / sin45° Next convert the sines to fraction shit a = 6sqrt(2)(sqrt(3)/2) / sqrt(2)/2 Next multiply recipricol so 2/sqrt(2) (THIS CANCELS EVERY 2 JAWNS) a =6sqrt(3) [ANSWER]

Solve the equation for exact solutions over the interval [0,2pi) 6cotx+5=-1

First subtract 5 onto -1 6cotx = -6 Next divide 6 onto -6 cotx = -1 Then find recipricol of the jawn so it will be tanx = -1 Finally, find tanx = -1 on unit circle (2 answers) {3pi/4 , 7pi/4}

Solve the equation on the interval [0 , 2pi) sin2x = sqrt(3) sinx

First subtract the jawn to get it to the left side sin2x - sqrt(3)sinx = 0 Next set sin2x = 2sinxcosx 2sinxcosx - sqrt(3)sinx =0 Next take out all the sines from the jawn sinx(2cosx-sqrt(3) = 0 Set the parenthesis = 0 sinx = 0 and 2cosx-sqrt(3)=0 next move the jawns over so it will be... sin x = 0 and cosx = sqrt(3)/2 Finally, solve the jawns {0 , pi , pi/6 , 11pi/6 }

Solve the triangle ABC, if the triangle exists B = 138.9° , c = 8.091, b = 15.234

sinC = 8.091sin(138.9°)/15.234 = 0.34914160 Next do the sin^-1 calculator jawn sin^-1(0.34914160) = 20.4° To find C subtract 20.4° from 180° = 159.6° (Add 159.6° to 138.9° to find that the sum is greater than 180° so there is only 1 solution) To find A we subtract 180° - 138.9 - 20.4° = 20.7 To find a we do... 15.234sin20.7°/sin138.9° a = 8.191 C = 20.4°, A = 20.7°, a = 8.191