APL 1 (week 1-4)

WEEK 1

100

What is Sine?

Opposite side of the angle divided by the Hypotenuse

Opposite/Hypotenuse  

200

Convert the angle in radians to degree.

π/5 radians

36 degrees

300

Find two positive and two negative angles using radian measure that are coterminal with 

π/6

1.  13π/6

2.  25π/6

3.  −11π/6

4.   −23π/6

400

Find the exact value of tan x if cos x=-(2/3) and x is not in quadrant III.

tan x =−√5/2

500

Find x. (round to the fourth decimal )

146.7314

WEEK 2

100

Find the exact value of the trigonometric function.

cos(π/6)

√3/2

200

State the reference angle for the given angle.

−110°

70°

300

If sin(t) = 78 and t is in the 2nd quadrant, find cos(t).

−√15/8

400

Use the given point on the unit circle to find the value of the sine and cosine of t.

sin(t) = √3/2

cos(t) = −1/2

500

If tan(t) = 43, and 0 ≤ t ≤ π/2, find the exact values of sin(t), cos(t), sec(t), csc(t), and cot(t).

sin(t)= 4/5

cos(t)= 3/5

sec(t)= 5/3

csc(t)= 5/4

cot(t)= 3/4

WEEK 3

100

Write each expression in terms of sines and/or cosines, and then simplify.

tan(x)/sec(x)

sin(x)

200

f(x) = cos(x). Solve f(x) = 12 on [0, 2π).

x = π/3,5π/3

300

Which of the following equations will shift y=cos(x) 

1. 3 units up          

2. Amplitude is 2    

3. Reflect it about the x-axis    

4.  to the right  

π/6

y=−2cos(x−π/6)+3

400

Write an equation of the form y=Asin[B(x-C)]+D whose graph is the given sine wave. 

y=2sin(2x)

500

Graph one cycle of y=tan(x) 

Period:

Domain: 

Range: 

Asymptotes: 

Period: 

π

Domain: 

(−π/2,π/2)(-π/2,π/2)

Range: 

(−∞,∞)(-∞,∞)

Asymptotes: 

x=−π/2, x=π/2

WEEK 4

100

Evaluate the expression.

sin^-1(√3/2)

π/3 radians 

200

Graph 

y=tan^-1(x)

Domain: 

Range:

Domain: 

(−∞,∞)(-∞,∞)

Range: 

(−π/2,π/2)

Graph: 

300

Evaluate the expression without using a calculator.

cos(sin^-1(3/5))

4/5

400

Use the fundamental identities to simplify the expression.

1 − cos²(x)/tan²(x) + 2 sin²(x)

sin²(x)+1

500

Function

(1/1 + cos(x)) − (1/1 − cos(−x)) = −2 cot(x) csc(x)

Prove or disprove the identity.

(1/1 + cos(x)) − (1/1 − cos(−x))=(1/1 + cos(x)) − (1/1 − cos(x))

a.

=(1/1 + cos(x)) · (1 − cos(x)1 − cos(x))− (1/1 − cos(x)) · ( ? / 1+ cos(x))

b.

=1 − cos(x) − ( ? ) / (1 + cos(x))(1 − cos(x)) 

c.

=−2 cos(x) / 1 − ( ? )

d.

=−2 cos(x) / (?)

e.

=−2 cos(x) / sin(x) · 1 / ( ? )  

f.

=−2 cot(x) ( ? )

G.

Is the Function an identity?

a (?)= 1+cos(x)

b (?)= 1+cos(x)

c (?)= cos²(x)

d (?)= sin²(x)

e (?)=sin(x)

f (?)= csc(x)

g.  It Is an identity