Math 240 Test 3 S/99

Math 240 Sample 2 (Find = all approximate answers to three significant digits)

1. Draw and solve for the following triangle: a=3D12cm, b=3D23cm, <C=3D19^o Ans:c » 12.3, <B»142^o

2. Draw and solve for the following triangle: &= lt;A=3D95^o, b=3D20cm, <C=3D17^o Ans:a » 21.5, c » 6.30

3. Draw and solve for the following triangle: a=3D30cm, b=3D20cm, c=3D43cm Ans: <C»117^o

4. Two earthquake detection stations A and B are 300 miles apart. Both stations detect an ear= thquake as shown. How far is the cent= er of the quake from each of the statons? Ans:512 and 357

5. Points A and B are on the opposite= sides of a lake. At a third point = C, the angle ACB is 43^o. = AC is 450 ft, BC is 853 ft. Find the distance AB. Ans: 607 ft=

6. The sides of a parallelogram are 21 and 15. = One of the angles between the two sides is 102^o. Find the length of the shorter diagonal. Draw. Ans: 23.1

7. Given that u =3D &l= t; 2, 3 >, v =3D < -1,4 >

a. Find the magnitude = of 2u – 4v Ans: 12.8 =

b. If A, B are two poi= nts, _{=3D u + v and B =3D (- 4,-5) what is the coordinate of A?
Ans: A=3D=
(-5,
-12)}

c. Use the dot product formula to find the angle between u and v.= Ans: 47.7^o

d. Use the dot product formula to find the angle between u+ v and u – v = Ans: 100^o

8. Given that u =3D < 4,-1 >, v =3D < 5, 4 >

a. Find the length of = the projection of v onto u. Ans: = 3.88

b. Find the length of = the projection of u onto v. Ans: = 2.50

c. Find the length of = the projection of u – v onto u + v. Ans: -2.53

9. Find the projection vectora in problem 10 a. b and c.

10. a. Give= n the v =3D <a, b> in quadrant II with | v | =3D 40, and the angle between v = and the negative y-axis is

134<= sup>o. Find a= and b. Ans: a=3D -28.8, b =3D 27.8

b. find = the angle between <-3, -5> and the positive y-axis. Ans: 149^o

11. a. Find the magnitude of the result= ant force of two forces of F =3D 45 newtons and G=3D112 newtons forming an angl= e of 87^o. Draw. Ans= :123 newton

b. Find the angle between the resultant and F. Ans: 65^o

c. Find the magnitude of equil= ibrant and the angle between the equilibrant and G. Ans: 158^o Let F =3D 35 newtons and G =3D 48 newtons be two forces acting at a point and t= heir resultant is 65 newtons. Find= the angle between F and G. Ans: <= /span>78^o

12. A force of 200lb is required to pu= ll a rock up an incline that makes an angle of 9^o. What is weight of the rock? Ans: 1278.5lb

13. A force of F=3D100lb makes an angl= e of 56⁰ with a second force G. The resultant makes an angle of 20^o with G. Find the magnitude of G. Ans: 171lb

14. Three forces of F=3D 45lb, G=3D84l= b and H=3D100lb acting at a point is in equilibrium. Find the angles between these forces. Ans: 83^o between F and = G, 154^o between H and G

15. (Find the exact and the approximate answer) If sin(A) =3D 2/5, and angle= A is in quadrant II, list the three trig. (SCT) = values and draw the angle. Ans: C=3D= -= Ö21/5 = » -0.917, T=3D -2/<= /span>= Ö21 = » -0.436

16. (Find the exact and the approximate answer) If csc(A) =3D -5, and angle = A is in quadrant III , list the three= trig. values (SCT) and draw the angle. Ans: S=3D -1/5, C =3D-= Ö24/5 = » -0.917, T=3D 1/Ö<= /span>24 = » 0.204

11. a. Draw the angle = arcsin(u) then simplify tan(arcsin(u))

b. Draw the angle arctan(3/u) then simplify sin(arctan(u))

5. Write down the formulas for circul= ar arc length, and area for a slice of a circle in terms of the central angle.

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6. Convert and draw the angles in a, = b on the unit circle. Label the coordinates of the point on the circle and list the sine, cosine and tangen= t of these angles :

Convert _{into degree=
=
b.
Convert -135^o into=
radian (=
leave
your answer in p.)}

7. A circular arc on a circle w= ith radius 5km has a length equal to 8 km, find the = central angle of this arc. (Give the answer in degree and in radian.) Ans: q =3D 8/5 rad = » 91.7^o

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8. A slice of pizza has a central angl= e of 25^o and the length of the its crust measured 4.5 inches. What is = the area of this slice? Ans: 23.2= inch²

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9. We have a pizza with 30-inch diameter. We cut a slice of p= izza measured 40 inch². What is the length of the pizza crust, along the edge? Ans: 5.33 inches

10. A slice of pizza has an area of 40= inch² with the crust measured 10 inches. What is central angle of this slice? (Give the answer in degree and = in radian.) Ans: 5/4 rad <= /span>= » 71.6^o

11. Simplify each expression and leave= the answer in sine and cosine.

a. cos²(x)tan²(x) = &nb= sp; = b. 1 – cot²(x)sin²(x)

Ans: sin²(x)<= span style=3D'mso-spacerun:yes'> = &nb= sp; = &nb= sp; Ans: sin²(x)

c. sin²(x)(1 – csc²(x)) = &nb= sp; d. tan²(x)(1 + cot²(x))

Ans: -cos^{2<=
/sup>(x)        =
            &nb=
sp;            =
            &nb=
sp;
Ans: 1/ cos²(x)}

e. (1 – sin(x)) (1 + sin(x)) = &nb= sp; f. (sec(x) + tan(x)) (sec(x) – tan(x))

Ans: cos²(x) = &nb= sp; = Ans: 1

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12. Sketch the following graphs. Label the following: a. end points<= span style=3D'mso-spacerun:yes'> b. the mid-line c. the vertices (high points and l= ow points) Indicate = the new period and sketch at least one period.

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a. y =3D - 2cos(x)+5 = &nb= sp; = b. y =3D -4sin (x + π ) + 2

y<= span lang=3DES style=3D'font-size:12.0pt;font-family:"Times New Roman";mso-ansi-= language: ES'> =3D 3 sin(3x – π/2) + 1 = &nb= sp; = d. y =3D -4 cos (x + π/4) + 2

&nb= sp; = &nb= sp; = &nb= sp; = &nb= sp;

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13. Given that csc(A) =3D -7/3 and A is the IV quadrant. Draw a reference triangle of A and= find the sine, cosine and tangent of A. &n= bsp; Ans: cos(A) =3D -Ö40 / 7, tan(A) =3D 3/7