Test sine, cosine and tangent of sum and difference of fourteen angles.
First, multiple choice questions
1.D 2。 C 3。 C 4 explosive B 5。 B
Tip:
3 . cos(- 15)= cos(30-45)= cos 30？ cos45 +sin30？ sin45
.
5. from tanatanb > 0, we know that a and b can't be obtuse or acute.
Also, A and B can't both be obtuse, so A and B are both acute.
From tanatanb < 1, we get, COSA > 0, COSB > 0,
So sinAsinB0 > 0, cos (a+b) > 0,
So, cos (? -c) > 0, that is, COSC < 0, so c is an obtuse angle △ABC is an obtuse triangle.
Second, fill in the blanks
6.3 7.8.9. 10.。
Tip:
9. Original form.
10.
=
= .
Third, answer questions.
1 1. Simple solution
12. Simple solution
.
13. Solution: =, so,
Therefore, the range of f(x) is [- 1, 2].
14. Solution:
From what is known, obtained,
So,,,
By, by, so,
therefore
Test sine, cosine and tangent of 15 times angle.
First, multiple choice questions
1.A 2。 D 3。 C 4 explosive B 5。 C
Tip:
4. It is known that SIN 76 = COS 14 = A, so, so.
5. It is known that cos < 0 is the third quadrant angle.
Therefore.
Second, fill in the blanks
6.7.8.9.4 10.[- 1, 1].
Tip:
7. Original formula =.
8. So t = 1, the range is.
10.=
= .
Third, answer questions.
Test paper reference answer
Unit test 1 basic elementary function 2
1-8 ADCDDCAB
9 10
10 2
1 1 √5
12 4
13 -4/3
14 8
15( 1)-2 (2) 13/4
16 (1) {x ≠ 2kπ π/3k belongs to z}
(2) Even function
17 omitted
18 3≤a≤4
Unit Test 2 Plane Vector
1-8DBBCACAC
9 -a+( 1/2)b
10 2
1 1 (3√ 10)/ 10
12 1
13 0
14 4/3
15 a=(4-2√3，2)
16 ( 1)m=4 (2)m≠6
17c (2,2) or (-6,6)
The value of 18 n p [-√3, 1]
Unit test 3 trigonometric identity transformation
1-8 DBDBADCB
9 -24/25
10 -7/25
1 1(-7√2)/26
12 √3
13 1/2
14 -4/5
15( 1)-4/3
(2)7/6
16( 1) 4/3 (2)- 16/65
17( 1)(0， 1) (2)√ 1-k
18 2 min max -2
(2) Even function
Compulsory 4-module test questions
1-8BBDBBACA
9 - 12/ 13
10 -√2/2
1 1 - 1/2
12 0
13 2π [π/3,4π/3]
The answer to 14 20 is not unique, for example, y =10sin ((π/8) x+3/4π)+20x belongs to [6, 14].
15 7/5
16( 1)m = 4(2)k =- 1
17 7/25
18( 1)π (2)a=π/2
19 ( 1)-8 (2)-√5/5
20( 1) 2co(2x+π/4)
(2)w=-2,-1 fai=2nπ+π/2 n belongs to z w= 1, 2ffai = (2n+ 1) π+π/2.
Xicheng 09- 10 The first semester of senior one mathematics.
Compulsory 4 Reference Answers
1- 10 BABBCDBCAB
1 1(4,-6)
12 -8
13 2π/3 or 4π/3
14 45
15 -4√2/7
16 π/3 a=π/3sin(2t+π/2) t belongs to [0, +∞).
17( 1) 1/2
(2)4
18( 1)Smax=4
(2) 16
19 (1) π (2)[kπ-π/8, kπ+3π/8] k belongs to Z.
Volume B 1 4
2 2
3 2 { 1≤x≤4}
4 ①②④
5 0 {0,- 1,-2,-3,-4,-5}
6 odd function
7 a=2 b=3 m= 1
8A={-2}，B={-2}