IB Math SL 11
Unit 4 – Right Triangle Trig
Name _____________________________
DUE DATE:
12/12/12
Questions 1-3. Find the degree measure of each angle whose radian measure is given.
1)
10
9
2)
3
4
3) 3
Questions 4-6. Find the radian measure of each angle whose degree measure is given.
4) 120°
5) 160°
6) 396°
Questions 7-12. Determine the quadrant in which the angle of the given measure lies.
7) 140°
8) -340°
9) 500°
10)
4
3
11) 
5
18
12)
2
27
Questions 13-14. Determine two coterminal angles in radian measure (one positive and one negative)
for the given angle.
13)

12
14) 
11
4
Questions 15-16. Determine two coterminal angles in degree measure (one positive and one negative)
for the given angle.
15) 52°
16) -390°
Questions 17-19. Find sin  , cos  , and tan  if the terminal side of  passes through the given
point.
17) 3,4
18) 8,6
19)  2 3 ,2


IB Math SL 11
Unit 4 – Right Triangle Trig
Questions 20-22. Given the values of sin  and cos  , determine the quadrant in which  lies.
20) sin   
22) sin   
15
1
, cos   
4
4
21) sin  
5
2
, cos   
3
3
5
2 5
, cos  
5
5
Questions 23-33. Find the exact value without using a calculator.
23) sin 
26) sin
24) cos
5
3
27) tan 225 
 3 

 4 
30) tan  
 2 

 3 
29) cos 


3
4
32) 3 cos

6
 sin


6
33) tan( 315 )  tan 135
25) cos 210 
28) sin 315 
31) sin 45   cos 45 
IB Math SL 11
Unit 4 – Right Triangle Trig
34) Find the exact values of a coordinate on the unit circle when θ is 135°. [no calculator]
35) Find θ, when (𝑐𝑜𝑠 −
√3
, 𝑠𝑖𝑛
2
1
− 2). [no calculator]
36) From her position at ground level, Hayley notices that the angle of elevation of the top of a building
is 40°. When she moves 20 metres closer to the building, the new angle of elevation is 55°. Find
the height of the building.
37) Building X and Y are across the street from each other, 95m apart. From a point on the roof of
building X, the angle of depression to the base of Building Y is 55° and the angle of elevation to the
top of Building Y is 35°. How tall are the two buildings?
IB Math SL 11
Unit 4 – Right Triangle Trig
38) Find the equation of the line passing through the origin and point P. Find the value of θ to the
nearest degree.
5 3𝜋
2
39) Given that 𝑠𝑖𝑛𝜃 = − 6,
≤ 𝜃 ≤ 2𝜋, evaluate
(a) sin2θ
(b) cos2θ
𝑎
𝑏
40) Given that 𝑡𝑎𝑛𝑥 = , 𝜋 ≤ 𝑥 ≤
3𝜋
,
2
evaluate sin2x.
41) Solve 𝑓(𝑥) = 0 for −360° ≤ 𝑥 ≤ 360°.
42) Sketch 𝑓(𝑥) = −𝑡𝑎𝑛2𝜋𝑥 + 1
IB Math SL 11
Unit 4 – Right Triangle Trig
43) The depth, y metres, of sea water in a bay t hours after midnight may be represented by the
function
 2
y  a  b cos 
 k

t  , where a, b and k are constants.

The water is at a maximum depth of 14.3 m at midnight and noon, and is at a minimum
depth of 10.3 m at 06:00 and at 18:00.
Write down the value of
(a)
a;
(b)
b;
(c)
k.
44) Let f (x) = sin (2x + 1), 0 ≤ x ≤ π.
(a)
Sketch the curve of y = f (x) on the grid below.
y
2
1.5
1
0.5
0
0.5
1
1.5
2
2.5
3
3.5 x
–0.5
–1
–1.5
–2
(b) Find the x-coordinates of the maximum and minimum points of f (x), giving your answers
correct to one decimal place.
(Total 6 marks)