# trigonometry

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5.Find the complete exact solution of sin x = -√3/2.

10. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to
two decimal places.

12. Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two
decimal places.

19.Prove that tan^2a – 1 + cos^2a
 = tan^2 a sin^2 a.

29. Prove that tan B sin B + cos B = sec B.

• trigonometry -

5.
since sin(pi/3) = √3/2
and sin < 0 in QIII,QIV, you have
x = (2k+1)*pi+pi/3 and 2k*pi-pi/3

10.
cos2x (1 - 3sinx) = 0
cos2x = 0 or sinx = 1/3

cos 2x = 0:
2x = k*pi/2 where k is an integer
x = pi/4, 3pi/4, 5pi/4, 7pi/4

sinx = 1/3:
x = 0.34 or pi-0.34

12.
tanx = 1/2 (-1±√5)
= .618 or -1.618

so take arctan to get x

19.
tan^2-1+cos^2
= sec^2-2+cos^2
= (sec-cos)^2
= (1-cos^2)^2/cos^2
= (sin^2)^2/cos^2
= sin^2/cos^2 * sin^2
= tan^2 sin^2

29.
tan*sin + cos
= sin^2/cos + cos
= (sin^2+cos^2)/cos
= 1/cos
= sec

• trigonometry -

1.
John Yinger thinks that the natural-born clause should be removed because (1 point)

it makes international policy more difficult.
it goes against a central principle of American democracy.
it damages the relationship between American citizens and immigrant communities.

2.
What do natural-born citizens and naturalized citizens have in common? (1 point)

Both can run for president.
Both are citizens of the United States.
Both are born in the United States.

3.
Which statement shows a contrast between the two opinions in the first selection? (1 point)

The Constitution should be amended.
America is open to foreign-born citizens.
The president should be loyal to our country.

4.

You would expect an authoritarian person to
(1 point)

respect individual freedom.
ask for other people's opinions.
demand total obedience.

5.
When Nicholas Gage says Miss Hurd "nearly dragged" him onto his life's path, he is using (1 point)

comparison.
sequence.
hyperbole.

6.

In "The Teacher Who Changed My Life," the author is trying to persuade readers that
(1 point)

immigrants face lots of difficulties.
schoolteachers are not appreciated enough.
he owes his success to Miss Hurd.

7.
Which of the following sentences contains a compound predicate? (1 point)

The author's mother died to help her children emigrate.
Miss Hurd was strict, yet encouraging.
The author answered the phone and heard his teacher's voice.

8.

Which of the following sentences contains a compound subject?
(1 point)

The author and her sister were dropped at their new school.
The principal was a grim-looking man.
The author did not understand the purpose of hobbies and clubs.

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