This preview shows page 1. Sign up to view the full content.
Unformatted text preview: MAC1147: Quiz #11
12/1/2009
In the topright corner of a clean sheet of paper, write your name, UFID, and section
number. Please use a pen with blue or black ink. When you are nished, FOLD your paper
in half lengthwise and write your name on the back.
1. An airplane 5 miles in the air measures the angles of depression to two cars on a straight
highway to be 30◦ and 45◦ . What is the distance between the two cars, in miles?
After drawing an appropriate picture, the following equations are suggested by the two
right triangles:
tan 30◦
tan 45◦ =
= 5
x+ y
5
x , where x represents the distance from the rst car to the plane, and y represents the distance between the rst and second cars. The second equation quickly
gives x = 5, so plugging this into the rst equation gives:
√ √
√
5
3
=
⇒ y + 5 = 5 3 ⇒ y = 5( 3 − 1) miles.
3
5+y sin x
in nonfractional form.
1 − cos x
sin x(1 + cos x)
sin x(1 + cos x)
cos x
sin x 1 + cos x
1
·
=
=
+
= csc x+cot x
=
2
1 − cos x 1 + cos x
1 − cos2 x
sin x sin x
sin x 2. Rewrite 1
= sin x cos x
tan x + cot x
1
1
1
1
=
=
=
= sin x cos x
2
2
1
sin x cos x
tan x + cot x
sin x + cos x
+
sin x cos x
cos x sin x
sin x cos x 3. Verify the trigonometric identity: 1 ...
View
Full
Document
This note was uploaded on 12/27/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.
 Summer '08
 GERMAN
 Calculus

Click to edit the document details