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z = r cos f We can use algebra to rearrange this, getting cos f = z /r provided r 0 When we examine Fig 9-9, we can see that for any given point P, the absolute value of z can never exceed r, so we can be sure that 1 z /r 1 Therefore, we can take the Arccosine of both sides of the preceding equation, getting Arccos (cos f) = Arccos (z /r) Simplifying, we obtain f = Arccos (z /r)

540 377

This formula works nicely if we know the value of r But we sometimes want to find the vertical angle in terms of x, y, and z exclusively We ve found that r = (x2 + y2 + z2)1/2 so we can substitute to obtain f = Arccos [z / (x2 + y2 + z2)1/2]

Why Write DMX Queries Where to Create and Test DMX Queries Where to Use DMX Queries in PowerPivot DMX Examples Cases Query: Nested Table Failure Cases Query: Flattened Table Success Cases Query on Specific Columns Content Query with DMX Subquery Content Query with Embedded Single Quotes Prediction Query with Embedded Single Quotes Prediction Forecast Query with Embedded Single Quotes SQL Used to Format and Manipulate the DMX Result Set

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P = (q,f,r) = (3p /2,p /2,5) Let s find the equivalent coordinates in Cartesian xyz space We ll start by calculating the x value The formula is x = r sin f cos q When we plug in the spherical values, we get x = 5 sin (p /2) cos (3p /2) = 5 1 0 = 0 The formula for y is y = r sin f sin q Plugging in the spherical values yields y = 5 sin (p /2) sin (3p /2) = 5 1 1 = 5 The formula for z is z = r cos f When we put in the spherical values, we get z = 5 cos (p /2) = 5 0 = 0 In xyz space, our point can be specified as P = (0, 5,0)

The number of matches for the SSRM project s attributes ranges from 0 for Organization Type Education and Used JAD Yes, up to 12 for Web Development Yes Although Jenny would have preferred to have a larger number of matches for several of the project attributes, she decides that the total number of matching projects is adequate to provide indicative estimates She also decides not to eliminate any further attributes from her analysis Jenny generates the SSRM project delivery rate (PDRCE) and speed of delivery (SDCE) estimates by calculating the averages (that is, the means) of the sets of project delivery rates and speeds of delivery for the conservative, likely, and optimistic values Finally, she combines the project delivery rate and speed of delivery estimates with SSRM s functional size of 540 function points

Another example Let s convert the xyz space point ( 1, 1,1) to spherical coordinates To find the radius, we use the formula

.

r = (x2 + y2 + z2)1/2

Plugging in the values, we get r = [( 1)2 + ( 1)2 + 12]1/2 = (1 + 1 + 1)1/2 = 31/2 To find the horizontal angle, we use the formula q = p + Arctan ( y /x) because x < 0 and y < 0 When we plug in the values for x and y, we get q = p + Arctan [ 1/( 1)] = p + Arctan 1 = p + p /4 = 5p /4 To find the vertical angle, we can use the formula f = Arccos (z /r) We already know that r = 31/2, so f = Arccos (1/31/2) = Arccos 3 1/2 Our spherical ordered triple, listing the coordinates in the order P = (q,f,r), is P = [5p /4,(Arccos 3 1/2),31/2]

All of the macro-estimation techniques presented in this book can be applied with both approximate and detailed functional sizing However, as the graph shows, the precision of the resultant estimates will improve as the precision of the functional sizing improves

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