# Answers to Exam 1 Practice Questions Section 5.1 a. b φ 8 sin(A)φ3 Answers to Exam 1 Practice Questions Section 5.1

a.

b = 8 sin( A ) = 3 = 5 ; cos( A ) = 4 = 5 ; tan( A ) = 3 = 4 csc( A ) = 5 = 3 ; sec( A ) = 5 = 4 ; cot( A ) = 4 = 3 b.

= 41 : 8 , so sin( ) = 0 : 67 ; cos( ) = 0 : 75 ; tan( ) = 0 : 89 c.

sec(30 ) = 2 p 3 sec( ) = 1 : 33 ; cot( ) = 1 : 12 ; cot(45 ) = 1 3 d.

e.

f.

77 = 60 = 30 ; cos g.

g.

1 : 04 1 : 7 Section 5.2

a.

B = 61 26 0 ; c b. About 606 f t = 36 : 2 ; b = 31 : 8 c. About d. About 92 : 9 cm 45 f t e.

f.

3 : 3 5 : 9 Section 5.3

a.

b.

c.

d.

635 10 0 ; sin( ) = 995 10 3 = 4 ; 0 ; 84 50 0 ; cos( ) = p 7 csc( ) = sin( ) = csc( ) = 60 ; p 3 2 4 = 3 ; sec( ) = 4 p p 41 41 4 41 ; ; cos( ) = sec( ) = 444 50 0 4 4 7 7 ; p 5 5 ; tan( ) = cot( ) = p 41 41 ; 41 ; 3 p 7 p 7 7 3 tan( ) = 4 cot( ) = 5 = 4 = 5 e. SInce 27 and 333 are both 27 from the positive x-axis, their trig function values should be the same, but since the two angles are in di¤erent quadrants, the signs of those trig function values will di¤er. Since 27 is in the …rst quadrant, it’s x- and y-coordinates are positive. That means sin(27 ) Since ; 333 cos(27 ) and tan(27 ) , as well as their reciprocals, will all be positive.

is in the fourth quadrant, it has a positive x-coordinate and a negative y-coordinate. This means cos(333 ) and sec(333 ) will be positive, 1

but all its other trig function values will be negative. Check this for yourself by using your calculator.

f. The plane is about 50 miles north and about 87 miles west of the airport.

g.

193 : 8 Good luck to all of you. I’m sure you’ll get the grade you deserve for all your hard work and e¤ort. Remember, there will be no SI sessions on September 9th or 11th.

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