Homework 0. Show all work. 1) Integrals: solve the first three by variable substitution, the last by...

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Homework 0. Show all work. 1) Integrals: solve the first three by variable substitution, the last by algebraic manipulation. For the first two describe the limits B ! 1 and a ! 0. Z B B dx(x2 + a2 ) 3/2 , Z B 0 dx ax (a2 + x2)3/2 , Z ? 0 d? sin ? 1 pa + b cos ? , Z dx 1 x2(x2 + a XXXXXXXXXXTrigonometry: a point on a circle has coordinates (x, y) = (0.82, XXXXXXXXXXFind the cosine of the angle ? between the y axis and the vector joining the origin and the point. what is the period of the function f(t) = 21 cot (13t + 29)? given a triangle of sides a, b, c, find the value of cot ? where ? is the angle between a, b. Express the function f(x) = sin 6x/ sin 3x as a function of sin x, cos x. Find the solutions for 2 cos3 ? cos ? = 0 in the interval [?, 0]
	
Document Preview: Homework 0. Show all work.
1) Integrals: solve the ?rst three by variable substitution, the last by algebraic manipu-
lation. For the ?rst two describe the limits B!1 and a! 0.
Z
B
2 2   3/2
dx(x +a ) ,
  B
Z
B
ax
dx ,
2 2 3/2
0 (a +x )
Z
?
1
d? sin? p ,
0 a+bcos?
Z
1
dx .
2 2 2
x (x +a )
2) Trigonometry:
apointonacirclehascoordinates(x,y)=(0.82,0.57). Find the cosine of the angle ?
between the y  axis and the vector joining the origin and the point.
what is the period of the function f(t)=21cot(13t+29)?
given a triangle of sides a,b,c, ?nd the value of cot? where ? is the angle between a,b.
Express the function f(x)=sin6x/sin3x as a function of sinx,cosx.
3
Find the solutions for 2cos ?   cos? =0intheinterval[  ? ,0].
Apoint a=(a,0),a

David · Accepted Answer

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2) The point is (0.82, 0.57)
If u is the angle between y axis and the vector and v the angle between x axis and 
the vector 
Then tan v = cot u = y/x = 0.57/0.82 = 0.6951 
cosec
2
v = 1+0.6951
2
= 1.4832 
sin v = 1/ rt of cosec
2
v = 0.8211 
what is the period of the function f(t) = 21 cot (13t + 29)? 
Period of cot t = pi 
Hence period of cot 13t = pi/13 
given a triangle of sides a, b, c, find the value of cot ✓ where ✓ is the angle 
between a, b.

Homework 0. Show all work. 1) Integrals: solve the first three by variable substitution, the last by algebraic manipulation. For the first two describe the limits B ! 1 and a ! 0. Z B B dx(x2 + a2 )...

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