WorksheetsGiá Trị Lượng Giác
Total questions: 125
Worksheet time: 3hrs 48mins
Define the trigonometric value of an angle (arc).
What is the sign of the trigonometric values for angle a in the range 0 to 180 degrees?
What is the relationship between the trigonometric values of two complementary angles?
What are the trigonometric values of special angles?
What are the basic trigonometric identities?
Calculate the value of the following expressions: a) (2 sin 30° + cos 135° - 3 tan 150° - cos 180° - cot 60°); b) (sin 90° + 2 cos 120° + cos 0° - tan 60° - cot 135°); c) (2 cos 60° + sin 30° + cos 30°).
Simplify the following expression: a) (sin 100° + sin 80° + cos 16° + cos 164°). b) (2 sin 180° - cot cos 180° + tan α - cot 180°) where 0° < α < 90°.
Prove the following identities: a) sin²α + cos²α = 1; b) (1 + tan²α) = (1/cos²α); c) (1 + cot²α) = (1/sin²α) for 0° < α < 180°.
Given the angle α where 0° < α < 180° satisfies tan 3α = 0. Calculate the value of the expression P = (2 sin 3α - 3 sin 2α) / (cos 3α + sin 2α).
Calculate the values of the following expressions: a) sin 90° + cos 90° + cos 180°; b) (2 sin 90° - 2 cos 60° - 3 tan 45°); c) (sin 45° - 2 sin 50° + cos 45° - 2 sin 40° - tan 55° - tan 35°).
Calculate the values of the following expressions: a) sin 3° + sin 15° + sin 75° + sin 87°; b) cos 0° + cos 20° + cos 40° + ... + cos 160° + cos 180°; c) tan 5° + tan 10° + tan 15° + ... + tan 80° + tan 85°.
What is the value of cos 60° + sin 30°?
Giá trị của oo cos 60sin 30 bằng bao nhiêu?
3/2
3
3/3
1
Giá trị của oo tan 30cot 30 bằng bao nhiêu?
4/3
13/3
2/3
2
Trong các đẳng thức sau đây, đẳng thức nào sai?
oo sin 0cos 01=1
oo sin 90cos 901=1
oo sin180cos1801=−1
oo sin 60cos 601=1
Trong các khẳng định sau, khẳng định nào sai?
oo cos 60sin 30=1
oo cos 60sin120=1
oo cos 30sin120=1
oo sin 60cos120=−1
Đẳng thức nào sau đây sai?
oo sin 45sin 452=1
oo sin 30cos 601=1
oo sin 60cos1500=1
oo sin120cos 300=1
Giá trị oo cos 45sin 45 bằng bao nhiêu?
1
2
3
0
Trong các đẳng thức sau, đẳng thức nào đúng?
(o sin 180cosα)=−sinα
(o sin 180sinα)=−sinα
(o sin 180sinα)=sinα
(o sin 180cosα)=cosα
Trong các đẳng thức sau, đẳng thức nào sai?
oo sin 0cos 00=1
oo sin 90cos 901=1
oo sin180cos1801=−1
oo 31 sin 60cos 60 2 + =1
Cho α là góc tù. Điều khẳng định nào sau đây là đúng?
sin0<α
cos0>α
tan0<α
cot0>α
Giá trị của ooo sin 36 cos 6 sin126 cos 84E là
1/2
3/2
1
1−
Giá trị của biểu thức oo22 2 2oo sin51 sin55 sin39 sin35A là
3
4
1
2
What is the value of the expression sin51 + sin55 + sin39 + sin35?
3
4
1
2
What is the value of the expression tan1 + tan2 + tan3 ... + tan88 + tan89?
0
2
3
1
What is the sum of sin2 + sin4 + sin6 + ... + sin84 + sin86 + sin88?
21
23
22
24
What is the value of tan5 * tan10 * tan15 ... * tan80 * tan85?
2
1
0
1
What is the value of cos73 + cos87 + cos3 + cos17?
2
2
2
1
Given sin(α) = 1/3 with 0 < α < 90, calculate cos(α) and tan(α).
Given cos(α) = -2/3 and sin(α) > 0, calculate sin(α) and cot(α).
Given tan(γ) = -2, calculate the remaining trigonometric values.
Given cos(α) = 3/4 with 0 < α < 90, calculate tan(3α) + cot(α).
Given tan(α) = 2, calculate the expression 3sin(α) - sin^3(α) + sin^2(α).
Given sin(x) + cos(x) = m, find sin(x) - cos(x).
Given cos(x) = 1/2, calculate the expression 3sin^2(x) + 4cos^2(x).
13/4
7/4
11/4
15/4
Given cos(α) = 1/3, what is the correct value of 2sin^2(α) + cos^2(α)?
1/3
10/9
11/9
4/3
Given tan(α) = 1/2, calculate cot(α).
cot(2α) = 1
cot(2α) = 2
cot(4α) = 1
cot(2α) = 1/2
Given cos(α) = -2/3 and 0 < α < 2π, calculate tan(α).
5/4
5/2
5/2
5/2
Given tan α = 1. Calculate cot α.
cot²α = 1.
cot²α = 2.
1/cot 4α = 1.
1/cot 2α = 1.
Given cos 3α = -2 and 0 < α < 2π. Calculate tan α?
5/4.
-5/2.
5/2.
-5/2.
Let α be an obtuse angle and sin α = 5/13. What is the value of the expression 3sin²α + cos α?
3.
9/13.
3 - 1.
9/13.
Given sin α + cos α = 1. What is the value of sin α . cos α?
2sin α . cos α = 1.
sin α . cos²α = 1.
2(1 - sin²α) = 1.
2(1 - sin²α) = 1.
Given cos 3α = -2. Calculate the value of the expression cot 3α + tan 2cot tan α.
19/13.
19/13.
25/13.
25/13.
Given cot 5α = 1. Calculate the value of 2cos²5α + sin α + cos α.
10/26.
100/26.
50/26.
101/26.
Given cot 3α = 1. What is the value of the expression 3sin 4cos 2sin 5cos α?
15/13.
13 - 1.
15/13.
13.
Given cos 3α = -2. What is the value of the expression cot 3α - tan 2cot tan α?
25/3.
11/13.
11/3.
25/13.
Given sin cos 2α + 1 = 3. What is the value of 4sin cos α?
3/2.
1/2.
1 - 1.
0.
Given tan α + cot α = m. Find m such that tan α + cot α = 22.
9m = 1.
3m = 1.
3m = -1.
3m = ±1.
Given 3cos α - sin α = 1. What is the value of tan α?
4tan α = 3.
3tan α = 4.
4tan α = 5.
5tan α = 4.
Given 2cos 2α + sin α = 0. Calculate the value of cot α.
5cot α = 4.
3cot α = 4.
2cot α = 4.
2cot α = 2.
Given sin α + cos α = 1. What is the value of 22tan α + cot α?
5/4.
7/4.
Calculate the value of cot α.
5 cot 4 α =
3 cot 4 α =
2 cot 4 α =
2 cot 2 α =
Given that 1 + sin α cos α = 3, what is the value of P = tan α + cot α?
5/4 P =
7/4 P =
9/4 P =
11/4 P =
Given that 1 - sin α cos α = 5, what is the value of P = sin α + cos α?
15/5 P =
17/5 P =
19/5 P =
21/5 P =
Prove the following identities (assuming the expressions are valid): a) sin² x + cos² x = 1.
Prove the following identities (assuming the expressions are valid): b) 1 + cot x tan x = 1.
Prove the following identities (assuming the expressions are valid): c) tan x + tan x = 1.
In triangle ABC, prove that tan² B + sin² A = 2 sin A cos A.
Simplify the following expressions (assuming the expressions are valid): a) sin(90) - cos(180) + sin(1) + tan A.
Prove that the expression does not depend on x.
Which of the following identities is correct?
sin² α + cos² α = 1.
sin² α + cos² α = 1/2.
sin² α + cos² α = 1.
sin² α + 2cos² α = 1.
Which of the following identities is correct?
sin² α + cos² α = 1.
sin² α + cos² α = 1/2.
sin² α + cos² α = 1.
sin² α + cos² α = 1.
Which of the following identities is correct?
sin² α + cos² α = 1.
sin² α + cos² α = 1.
sin² α + cos² α = 1.
sin² α + cos² α = 1.
Which of the following identities is correct?
sin^2(α) + cos^2(α) = 1
sin^2(α) + cos^2(α) = 2
sin^2(α) + cos^2(α) = 1
sin^2(α) + cos^2(α) = 2
Simplify the expression (tan^2(x) + cot^2(x))
4A
1A
2A
3A
Which statement is false?
sin^2(α) + cos^2(α) = 1
(1 + cot^2(α))sin(α) ≠ 0
(tan(α) - cot(α))sin(α)cos(α) ≠ 0
(1 + tan^2(α))cos(α) ≠ 0
Simplify the expression 1 - sin^2(x) + cot^2(x)
2sin(x)
2cos(x)
1/cos(x)
cos(x)
Which of the following identities is false?
(sin^2(x) + cos^2(x)) = 1
(tan(x) - cot(x)) = 0
(sin^2(x) + cos^2(x)) = 2
(tan^2(x) + cot^2(x)) = 2
The expression tan^2(x) - sin^2(x) + cos^2(x) equals
1
0
2
1
The expression (cot(α) + tan(α)) equals
sin^2(α) - cos^2(α)
cot^2(α) + 2
sin^2(α) + cos^2(α)
cot^2(α) + 2
Simplify the expression (cot^2(x) + sin^2(x))
1A
2A
3A
4A
Simplify the expression cot(cos(sin(x))) = cot(x) + A.
1
2
3
4
The expression f(x) = 4sin^2(x) + 6cos^2(x) has a value of:
1
2
3
0
The expression g(x) = 4cos^2(x) + 2sin^2(x) has a value of:
1
2
2
1
Which of the following statements is false?
sin^2(x) + cos^2(x) = 1
sin(2x) = 2sin(x)cos(x)
sin(x) + cos(x) = 1
sin^2(x) + cos^2(x) = 1
Without using a table or calculator, calculate the value of the following expressions: a) (2 sin 30 + cos 135 - 3 tan 150 - cos 180 - cot 60); b) (2 sin 90 + 2 cos 120 - 2 tan 60 + cot 135); c) (2 cos 60 + sin 30 + cos 30).
Simplify the following expression: sin100 + sin80 + cos16 + cos164.
Prove the following identities: 1 + sin^2(α) = cos^2(α).
Given the angle α where 0 < α < 180, satisfy tan(3α) = 0. Calculate the value of the expression P = (2sin^3(α) - 3sin^2(α)cos(α)) / (3sin^2(α) + 2cos^3(α)).
Calculate the value of the following expressions: a) sin 90 + cos 90 + cos 180 b) 3 sin 90 - 2 cos 60 - tan 45 c) sin 45 - sin 50 + cos 45 - sin 40 + tan 55 - tan 35
Calculate the value of the following expressions: a) sin 3 + sin 15 + sin 75 + sin 87 b) cos 0 + cos 20 + cos 40 + ... + cos 160 + cos 180 c) tan 5 + tan 10 + tan 15 + ... + tan 80 + tan 85
What is the value of cos 60 + sin 30?
What is the value of cos 60 + sin 30?
3/2
3
3/3
1
What is the value of tan 30 + cot 30?
4/3
13/3
2/3
2
Which of the following identities is incorrect?
sin 0 + cos 0 = 1
sin 90 + cos 90 = 1
sin 180 + cos 180 = -1
sin 60 + cos 60 = 1
Which of the following statements is incorrect?
cos 60 = sin 30
cos 60 = sin 120
cos 30 = sin 120
sin 60 = -cos 120
Which of the following identities is incorrect?
sin 45 + sin 45 = 2
sin 30 + cos 60 = 1
sin 60 + cos 150 = 0
sin 120 + cos 30 = 0
What is the value of cos 45 + sin 45?
1
2
3
0
Which of the following identities is correct?
sin(180 - α) = -sin(α)
sin(180 - α) = sin(α)
sin(180 - α) = -sin(α)
sin(180 - α) = sin(α)
Which of the following identities is incorrect?
sin 0 + cos 0 = 1
sin 90 + cos 90 = 1
sin 180 + cos 180 = -1
sin 60 + cos 60 = 1/2
If α is an obtuse angle, which of the following statements is true?
Given that α is an obtuse angle. Which of the following statements is true?
sin(0) < α
cos(0) > α
tan(0) < α
cot(0) > α
What is the value of sin(36) cos(6) sin(126) cos(84)?
1/2
3/2
1
1-
What is the value of the expression sin(51) + sin(55) + sin(39) + sin(35)?
3
4
1
2
What is the value of tan(1) tan(2) tan(3) ... tan(88) tan(89)?
0
2
3
1
What is the sum of sin(2) + sin(4) + sin(6) ... + sin(84) + sin(86) + sin(88)?
21
23
22
24
What is the value of tan(5) tan(10) tan(15) ... tan(80) tan(85)?
2
1
0
1-
Given sin(α) = 1/3 with 0 < α < 90. Calculate cos(α) and tan(α).
Given cos(α) = -2/3 and sin(α) > 0. Calculate sin(α) and cot(α).
Given tan(γ) = 2. Calculate the remaining trigonometric values.
Given cos(α) = 3/4 with 0 < α < 90. Calculate tan(3α) + cot(α).
Given tan(α) = 2. Calculate (3sin(α) - sin^3(α)) / (sin^2(α) + cos^2(α)).
Given that cos(x) = 1/2. Calculate the expression 3sin^2(x) + 4cos^2(x).
13/4
7/4
11/4
15/4
Given that cos(α) = 1/3. The correct value of the expression sin^2(α) + cos^2(α) is:
1/3
10/9
11/9
4/3
Given that tan(α) = 1/2. Calculate cot(α).
cot^2(α) = 1
cot^2(α) = 2
cot(α) = 1/4
cot(α) = 1/2
Given tan^2(α) = 1. Calculate cot(α).
cot^2(α) = 1
cot^2(α) = 1
1/cot(4α) = 1
1/cot(2α) = 1
Given cos^2(α) = -2 and 0 < α < 2π. Calculate tan(α)?
5/4
-5/2
5/2
-5/2
Given α is an obtuse angle and sin(α) = 5/13. What is the value of the expression 3sin^2(α) + 2cos(α)?
3
9/13
3
9/13
Given sin(α) + cos(α) = 1. What is the value of sin(α) * cos(α)?
2sin(α) * cos(α) = 1
sin(α) * cos^2(α) = 1
2/1sin(α) * cos(α) = 2
2/1sin(α) * cos(α) = 2
Given cos^2(α) = -2. Calculate the value of the expression cot(3α) + tan(2α)?
19/13
19/13
25/13
25/13
Given cot(5α) = 1. Calculate the value of the expression 2cos^2(5α) + sin(α)?
10/26
100/26
50/26
101/26
Given cot(1/3α) = 1. What is the value of the expression 3sin^4(α)?
Given that 1/cot(3α) = 3sin(4α) + 2sin(5α)cos(α), what is the value of the expression?
15/13
13
15/13
13
Given that 2cos(3α) = -1, what is the value of the expression cot(3α) - tan(2cot(α))?
25/3
11/13
11/3
25/13
If sin(α) + cos(α) = 2, what is the value of 4sin(α)cos(α)?
3/2
1/2
1
0
Given that tan(α) + cot(α) = 7, find m such that 2tan(α)cot(α) = 9m.
9m = 9
3m = 3
3m = -3
3m = ±3
Given that 3cos(α) - sin(α) = 1, what is the value of tan(α)?
4tan(α) = 3
3tan(α) = 4
4tan(α) = 5
5tan(α) = 4
Given that 2cos(2α) + sin(2α) = 0, calculate the value of cot(α).
5cot(α) = 4
3cot(α) = 0
Given 2cos^2(α) + sin^2(α) = 1, find the value of cot(α).
5 cot(4α) = 1
3 cot(4α) = 1
2 cot(4α) = 1
2 cot(2α) = 1
Given 1 + cos(α)sin(α) = 3, what is the value of P = tan(α) + cot(α)?
5/4 P = 1
7/4 P = 1
9/4 P = 1
11/4 P = 1
Given sin(α) - cos(α) = 5, what is the value of P = sin(α) + cos(α)?
15/5 P = 1
17/5 P = 1
19/5 P = 1
21/5 P = 1
Prove the following identities (assuming the expressions are valid).
Prove the following identities (assuming the expressions are valid): a) 2sin(x)cos(x) = sin(2x) b) 1 + cot(x) = 1/(1 - cot(x)) c) tan^2(x) + 1 = sec^2(x)
Given triangle ABC. Prove that tan(B) = (sin(A)cos(B) + cos(A)sin(B))/(cos(A)cos(B))
Simplify the following expressions (assuming the expressions are valid): a) sin(90) - cos(180) + tan(A) b) 1 + sin(B) - cos(1)
