Final Review

Ch. 6

100

cos(tan^-11)

sqrt (2) /2

200

Cos^-1(tan 3pi/4)

pi

300

Cos(2sin^-1sqrt 3 /2)

-1/2

400

Sec 5pi/6

-2sqrt 3/3

500

Tan 5pi/3

-sqrt 3

Ch. 7

100

Simplify:

cotxtanx+sinxsecx

1 + Tanx

200

Simplify:

secx- cosx

tanxsinx

300

In quad I, 

Find Sin(x+y), if cosx =2/5 and siny= 3/4

(7sqrt 3 + 6)/20

400

In Quad. I, Cos x= 2/7.

Find sin 2x, Cos 2x, tan 2x

sin 2x= 12 sqrt 5/49

Cos 2x= -41/49

Tan 2x=-12sqrt 5/41

500

Solve[0,2pi]:

4sin²x+2cos²x=3

pi/4,3pi/4,5pi/4,7pi/4

Ch. 6 & 7

100

Solve

4cos²x-2=0

pi/4, 3pi/4,5pi/4, 7pi/4

200

Solve [0,2pi]:

3cos²x=6cosx-3

0,2pi

300

Write a cosine equation:

amp=20

pd=pi/2

ps=2pi

vs=4

y= +/- 20 cos(4x-8pi)+4

400

y= sin(x/2+pi/2)-3

Find the amp, pd, ps, and vs.

amp=1

pd=4pi

ps=-pi

vs=-3

500

Simplify:

(tanx/ sinx)     + (1/cosx)

2sec x

Ch. 11

100

Simplify:

a) ((3f)^-2)³

b) 27^1/220^1/2

a)1/729f⁶

b) 6sqrt15

200

Solve for a:

4log₈2+(1/3)log₈27=log₈a

48

300

Simplify:

log₄sqrt4

1/2

400

Solve:

6^x=2^x-1

-.631

500

Solve:

16=10(1+e^x)

-.511= ln. 6

Ch. 5

100

Given (-2,3) lies on the terminal side-

Find the 6 trig functions.

sin x=3/sqrt 13

cosx=-2/sqrt 13

Tan x=-3/2

cot x= -2/3

csc x= sqrt 13/3

sec x= sqrt 13/-2

200

Given rt. triangle MPN (<P=rt angle)-

If n=15 and m=9, find <N.

59degrees

300

At a local airport, a light that produces a white-green beam is placed on the top of a 45 ft tower.  If the tower is at one end of the runway, find the angle of depression needed so that the light extends to the end of the 2200 ft runway.

1.2 degrees

400

Solve for all real values:

2sec²x-tan⁴x=-1

pi/3 + pi n   and 5pi/3 + pi n

500

Solve [0,2pi]

4sin²x+1=-4sinx

7pi/6 and 11pi/6