Name __________________________________ A2 HW – Review of Trig

Use the triangle to find each of the ratios:

1) sin θ = _________

2) cos θ = ________

3) tan θ = ________

Using the triangle, approximate the trig ratio to the nearest hundredth:

4) tan A = ________

5) sin B = ________

6) cos A = _______

7) A flagpole casts a shadow that is 13 meters long. If the pole is 16 meters high,

what is the angle of elevation from the end of the shadow to the top of

the pole?

8) A contractor is constructing a ramp at a local senior citizens center. She knows that

the ramp needs to be 20 feet long and it rises to a height of 4 feet. To the nearest

tenth of a degree, find the measurement of the angle that the ramp makes with the

ground?

75

50

25

θ

6.0 4.8

3.6

A

C B

Give the measure of the acute angle θ to the nearest degree:

9) sin θ = 14

9 10) cos θ = .96

11) tan θ = 3

2 12) sin θ = .62

13) If sin θ = 3

3, find the exact value of each of the following.

a. cos θ b. tan θ

14) The axis of symmetry of the equation y = x2 + 3x – 5 is:

(1) x = 0 (2) x = 2

3− (3) x = 29 (4) x =

2

3

15) What is the inverse of the function y = 2x in y = form?

(1) y =

X

2

1

(2) y = x

1

2 (3) y = log 2 x (4) x = 2y

Name __________________________________ A2 HW – Unit Circle #1

Determine in which quadrant an angle of the given measure lies:

1) 215° 2) -110° 3) 318°

4) 72° 5) -45° 6) 422°

7) -240° 8) 812° 9) -500°

For each given angle, find a coterminal angle:

10) 36° 11) -181° 12) 450°

13) Which angle is not coterminal to 112°?

(1) -248° (2) 68° (3) 472° (4) 832°

14) The coordinates of any point on the unit circle are (x, y) or ( _______, _______).

Using the unit circle, give the exact value of each. Do not use a calculator:

15) sin (-270°) 16) cos 540° 17) sin 3600°

18) sin 450° 19) cos (-90°) 20) cos 270°

21) If cos θ = 4

7, find the exact value of each of the following:

a. sin θ b. tan θ

22) Drew Stafford takes a slap shot 20 feet from the net. If the shot rings off the left goal

post 3 feet above the ice, what would be the angle of elevation of the path of the

puck? Round to the nearest hundredth.

23) If f(x) = 3x – 6, find f-1(x).

24) If log 5 = x and log 6 = y, express in terms of x and y: log 25

30

20

3

Name _________________________________ A2 HW – Unit Circle #2

According to the unit circle, in what quadrants is:

1) cos θ is negative 2) tan θ is positive 3) sin θ is positive

Which quadrants would the terminal side of the given angle lie in if:

4) sin θ < 0 5) cos θ = .5612 6) tan θ > 0

Refer to the drawing at the right of the unit circle with the given points on it. Give the letter

that could represent the value:

7) sin –310° 8) cos 0°

9) cos 80° 10) cos 50°

11) sin 440° 12) sin 1080°

13) cos -670° 14) sin 0°

Use the unit circle at the right to find the value:

15) cos α 16) sin θ

17) α 18) θ

For the indicated point, tell if the value is for sin θ or cos θ and then if it is positive, negative,

or neither:

19) a 20) b 21) c

22) d 23) e 24) f

To the nearest thousandth, find the image of the point (1, 0) under the given rotation:

25) R256 26) R117 27) R6

28) A ship on the ocean surface detects a sunken ship on the ocean floor at an angle of depression of 50°. The distance between the ship on the surface and the sunken ship

on the ocean floor is 200 meters. If the ocean floor is level in this area, how far above

the ocean floor, to the nearest meter, is the ship on the surface?

29) If tan θ = 3

3, find the exact value of sinθ .

Name ___________________________________ A2 HW – Unit Circle #3

1) In the accompanying diagram of a unit circle,

BA is tangent to circle O at A, CD is

perpendicular to the x-axis, and OC is a radius.

Which distance represents sin θ ?

(1) OD (3) CD

(2) BA (4) OB

2) Give the letter in the diagram at the right that could represent the given value:

a) sin 138° b) cos (-68°)

c) cos 228° d) sin (-270°)

3) Circle O has its center at the origin, OB = 1, and OABA ⊥ . If m ∠ BOA = θ , which line

segment shown has a length equal to cos θ ?

4) Which angle is not coterminal with an angle of 242°?

(1) -118° (2) 62° (3) 602° (4) 118°

5) If 0° < θ < 360°, and sin θ = -0.8192 find, to the nearest tenth of a degree, the two

values of θ.

6) If tan θ = 1.4281 and 0° < θ < 360°, find to the nearest degree, the two values of θ.

7) If sin θ = 5

3, find the exact value of each of the following.

a. cos θ b. tan θ

8) Write the equation of a circle with a radius of 5 and a center at (-3, 8) in:

a) center-radius form

b) standard form

9) Simplify: 3 177yx108

Name ___________________________________ A2 HW – Unit Circle #4

1) If cos x = 2

2− , in which quadrants could ∠ x terminate?

(1) I and IV (2) I and III (3) II and IV (4) II and III

2) If θ is an acute angle such that sin θ = 13

5, what is the exact value of cos θ ?

3) Circle O has its center at the origin, OB = 1, and OABA ⊥ . If m ∠ BOA = θ , which line

segment shown has a length equal to cos θ ?

4) If sin B = 5

3− and cos B > 0, in which quadrant does ∠ B terminate?

(1) I (2) II (3) III (4) IV

5) If tan x = -1 and cos x = 2

2− , in which quadrant could angle x terminate?

(1) I (2) II (3) III (4) IV

6) If θ is an angle in standard position and its terminal side passes through the point

−−

2

3,

2

1 on the unit circle, then a possible value of θ is

(1) 60° (2) 120° (3) 240° (4) 210°

7) Point P(0.6,-0.8) is on unit circle O.

What is the measure of angle θ to the nearest degree?

(1) 143 (2) 53 (3) 323 (4) 307

8) If sin A < 0 and tan A > 0, in which quadrant does the terminal side of ∠ A lie?

(1) I (2) II (3) III (4) IV

9) If cos A < 0 and sin A > 0, in which quadrant does the terminal side of ∠ A lie?

(1) I (2) II (3) III (4) IV

10) In the accompanying diagram of a unit circle, the ordered pair, (x,y) represents the points where the terminal side of θ intersects the unit circle.

If θ = 120°, what is the value of y?

(1) 1 (2) 2

3 (3)

2

1− (4)

2

2−

11) Solve algebraically for x: 272x+1 = 94x

12) Simplify: 3 65yx375

Name ___________________________________ A2 HW – Reciprocal Functions Write each expression in terms of sin θ, cos θ, or both. Simplify wherever possible:

1) θ

θ

csc

cot 2) (tan θ )(csc θ )

3) (cot θ )(sin θ ) 4) θ

θ

sec

cos

Find the exact value of the expression:

5) csc 150° 6) sec 210° 7) cot 30°

8) If sec θ < 0 and sin θ > 0, in what quadrant will θ terminate?

Determine the quadrant in which x lies if:

9) csc x < 0 and cot x < 0 10) sec x > 0 and sin x < 0

11) If log 5 = k and log 6 = w, express the following in terms of k and w: log 6

30

12) Solve for x to the nearest thousandth: 4x-5 = 432

13) What is the sum and product of the roots of the equation 4x2 + 32 = 20x

14) What is the domain of the function f(x) = 9x

x2 2

−

?

(1) x = 9 (2) x > 9 (3) x ≠ 9 (4) x < 9

15) Simplify: 23h48g4

1

Name __________________________________ A2 HW – Exact Values

1) If sin x = 6

3, find the value of cos x and tan x.

2) If cos θ = 5

3− and θ is in the second quadrant, find the exact value of the 5 remaining

trigonometric functions:

3) If cot θ = 2

1− and θ is in the forth quadrant, find the exact values of the 5 remaining

trigonometric functions:

4) In the accompanying diagram, PR is tangent to circle O at R, ORQS ⊥ ,

and ORPR ⊥ .

Which measure represents cos θ ?

5) Write in terms of sine, cosine or both:

a) cscθ

secθ b) secθ + tanθ

6) If sec x = 3− , in which quadrants could angle x terminate?

(1) I and III (2) II and III (3) II and IV (4) III and IV

7) Refer to the diagram at the right. Give the letter that could stand for the function

value:

a) sin 180° b) sin 82°

c) cos 28° d) cos -270°

Name __________________________________ A2 HW – Sum/Difference of 2 Angles

1) Find the exact value of sin 105°

2) Which expression is equivalent to cos 100° cos 80° - sin 100° sin 80°?

(1) –1 (2) 0 (3) 1 (4) cos 20°

3) Find the exact value of sin 110° cos 40° + cos 110° sin 40°

4) Find the exact value of sin 310° cos 70° - cos 310° sin 70°.

5) The expression cos 40° cos 10° + sin 40° sin 10° is equivalent to

(1) cos 30° (2) sin 30° (3) sin 50° (4) cos 50°

6) What is the exact value of °°+

°−°

10tan250tan1

10tan250tan?

7) If sin A = 5

4, tan B =

12

5and angles A and B are in Quadrant I, what is the

value of sin (A + B)?

8) A and B are positive acute angles. If sin A = 5

4 and cos B =

17

8, find the value

of tan (A – B).

9) A population of wolves in a county is decreasing 2% a year. If there were 80 wolves in

1998. Predict the number of wolves in the population in the year 2008.

10) If the terminal ray of angle θ, in standard position, passes through the point whose

coordinates are

−

2

3,

2

1 , find m∠θ.

Name __________________________________ A2 HW – Double Angles

1) If tan θ = 5

12 and θ is a third quadrant angle, find the exact value of:

a) cos 2 θ

b) tan 2 θ

2) The expression 2 sin 30° cos 30° has the same value as

(1) sin 60° (2) sin 15° (3) cos 60° (4) cos 15°

3) The expression sec x sin 2x has the same value as

(1) 2 cos x (2) 2 (3) 2

1 (4) 2 sin x

4) Which expression is equivalent to x2sin

x2cos1+?

(1) tan x (2) cot x (3) –sin x (4) –cos x

5) Using the difference of two angles, find the exact value of sin15°

6) Use the unit circle below to determine which letter stands for the given value.

a) sin °− 348

b) cos °250

7) If 0° < θ < 360°, find, to the nearest degree, two values of θ for: cos θ = -0.5878

•

•

• (a, b) (c, d)

(e, f) (g, h)

Name __________________________________ A2 HW – Pythagorean Identity

1) If sinθ = 3

8, use the Pythagorean Identity to find the exact value of:

a) cos θ b) tan θ c) sec θ

2) If cos θ = 1

2, use the Pythagorean Identity to prove sinθ =

3

2.

3) Using the triangle at the right, verify the property:

(sin θ )2 + (cos θ)2 = 1

4) Given that θ =45°, verify the Pythagorean Identity.

5) Show that (sin θ )2 + (cosθ)2 = 1 is equivalent to (tan θ )2 + 1 = (sec θ)2.

1

2

θ

6) If csc θ < 0 and cos θ > 0, which might be the value of θ?

(1) 30° (2) 120° (3) 210° (4) 330°

7) If sin θ = 0.7660, find, to the nearest degree, two positive values of θ that are less

than 360°.

8) Write θ

θ

csc

cot in terms of sin θ, cos θ, or both and simplify.

8) Simplify: 3 4 954a b

9) A radioactive substance decays at the rate of 2 percent per year.

a) Write an equation to model the amount of material left after t years, if there

were initially 500 grams.

b) How long would it take until there were only 250 grams remaining?

Name __________________________________ A2 HW – Cofunctions

Write the expression as a function of a positive acute angle whose measure is less

than 45°:

1) sin 65° 2) cot 60° 3) sin 119°

Solve each equation for θ:

4) cot (3θ - 6)° = tan (θ + 8)° 5) csc (3θ - 8)° = sec (48 + 2θ)°

6) Which expression is equivalent to sec 48°?

(1) csc 42° (2) csc 48° (3) cos 42° (4) cos 48°

7) For what value of θ does cos (3θ + 25)° = sin (37 - θ)°?

(1) 28 (2) 23 (3) 14 (4) 7

8) Convert 112.532° to the nearest seconds.

9) Convert 205°17’10” to the nearest hundredth of a degree.

10) Write in terms of sine, cosine or both: cscθ

cossecθ

• θ

11) If sin θ = 1

3 and θ is in the second quadrant, find the exact values of the 5 remaining

trigonometric functions:

12) If tan θ = -9.5141, find to the nearest degree, two values of θ if 0° < θ < 360°.

13) The solution set to xx

1x4

1x

x

x

2x2

+

+=

++

− is

(1)

−2

1 (2) {3} (3)

− 3,2

1 (4) { }

14) Solve for x to the nearest hundredth: 5x = 401