Mathematics 5 SN TRIGONOMETRY PROBLEMS 2 If x , 4 3 , 3 2 , which one of the following statements is TRUE? A) sin x > 0 and cos x > 0 C) sin x < 0 and cos x > 0 B) sin x > 0 and cos x < 0 D) sin x < 0 and cos x < 0 If , 2 < t < 2 3 , which one of the following statements is TRUE? A) cos t > 0 and sin t > 0 C) cos t < 0 and sin t > 0 B) tan t > 0 and cos t < 0 D) sin t < 0 and tan t < 0 Given the functions f(x) = tan x and g(x) = sin x. What are the values for which the functions f and g are 0 in [0, ]? A) 0, 2 C) 2 , 0 B) 0, D) 0, 2 , 1 2 3
Transcript
Mathematics 5 SN
TRIGONOMETRY PROBLEMS 2
If x ,4
3 ,
3
2
, which one of the following statements is TRUE?
A)
sin x > 0 and cos x > 0
C)
sin x < 0 and cos x > 0
B)
sin x > 0 and cos x < 0
D)
sin x < 0 and cos x < 0
If ,2 < t < 2
3
, which one of the following statements is TRUE?
A)
cos t > 0 and sin t > 0
C)
cos t < 0 and sin t > 0
B)
tan t > 0 and cos t < 0
D)
sin t < 0 and tan t < 0
Given the functions f(x) = tan x and g(x) = sin x.
What are the values for which the functions f and g are 0 in [0, ]?
A)
0, 2
C)
2
, 0
B)
0,
D)
0, 2
,
1
2
3
What is the solution set of sin x 1 = 0 in ?
A)
{1}
C)
{x | x =
2 + n, n Z}
B)
2
D)
{x | x =
2 + 2n, n Z}
4
What is the solution set of the equation 2sin2x 4cos2x + 1 = 0 where x
2,
2
-?
A)
6 ,
6
-
C)
4
B)
3 ,
3
-
D)
4 ,
4
-
If x [0, 2π[, find the solution set of the following equations :
a) sin2x + cos x = 1
b) 2sin2x cos x 2 = 0
Show your work.
a)
Work
Result : The solution set is _______________.
5
6
b)
Work
Result : The solution set is _______________.
What are the zeros in the following equation if x [0, 2]?
2sin2x 1 = 0
A)
4
- ,
4
C)
4
7 ,
4
B)
4
3 ,
4
D)
4
7 ,
4
5 ,
4
3 ,
4
Which values of x belonging to
2
3,0 satisfy the equation 4 sin3x sin x = 0?
The values of x belonging to
2
3,0 and that satisfy the equation are
_______________________________________________.
7
8
2
3Sin x in the circle with centre O, show on the
right.
Furthermore, AB // OP and m OA = 1 unit.
What is the area of the shaded region?
Show all your work.
Show all your work.
Answer: The area of the shaded region is __________ square units.
x E
A
P
B
F O
x E
A
P
B
F O
9
Find all the solutions of the equation 2cos2x 3sin x 3 = 0 such that
x
2 ,
2
3 . Give your solution in radian measure.
Show all your work.
Show all your work.
2cos2x 3sin x 3 = 0 , x
2 ,
2
3 .
Answer:
The values of x in the domain are __________________ radians.
10
What are the exact values of A that satisfy the following trigonometric equation?
sin A cot A + 2 cos2 A = 1, A [0, 2]
Show all your work.
sin A cot A + 2 cos2 A = 1, A [0, 2]
Answer:
The solution is A = __________________.
11
Given the following trigonometric equation:
2 sin2 x + 5 sin x 3 = 0, x [0, 2]
What are the exact values of x that satisfy this equation?
The exact values of x are __________ and __________.
12
Strange geometric formations, known as crop circles, have appeared in fields around the world. The creators of
the crop circle shown below would like to surround their design with a border, in the shape of an equilateral
triangle.
The circles that were used to make the design are congruent to the circle whose equation is:
x2 + y2 6x 2y 26 = 0
The circles are externally tangent to one another and tangent to the border.
What is the length of the border?
Round your answer to the nearest hundredth of a unit.
Show all your work.
13
Show all your work.
Answer:
To the nearest hundredth of a unit, the border measures __________.
Given the trigonometric equation:
2 cos2x + cos x = 1, x [, ]
What are the exact values of x that satisfy this equation?
The exact values of x satisfying the given equation are:
