Warm ups.notebook
December 12, 2013
1
Warm ups.notebook
December 12, 2013
Warm Up
1.
Write a linear equation satisfying the given conditions:
f(-11) = 23 and f(-4) = -79
2.
Write as a single logarithm:
a) log x - 2log (x + 2) + 7log 2x
3.
b) 2log (x + 6) - 3[log (x - 2) + 4log x]
Evaluate (without a calculator)
a) sec 4π/3
b) csc 3π/4
c) cot 3π/2
d) sin π
e) cos 11π/6
f) tan 7π/4
2
Warm ups.notebook
December 12, 2013
Warm Up
1.
2.
3.
Write a linear equation satisfying the given conditions:
f(-11) = 23 and f(-4) = -79
(y - 23) = 102/-7(x + 11)
(y + 79) = 102/-7(x + 4)
Write as a single logarithm:
a) log x - 2log (x + 2) + 7log 2x b) 2log (x + 6) - 3[log (x - 2) + 4log x]
log ((x + 6)2/(x4(x - 2))3
log (x(2x)7)/(x + 2)2)
Evaluate (without a calculator)
c) cot 3π/2
b) csc 3π/4
a) sec 4π/3
-2
0
√2
f) tan 7π/4
e) cos 11π/6
d) sin π
-1
√3/2
0
3
Warm ups.notebook
December 12, 2013
Warm Up
1.
Write a linear equation satisfying the given conditons:
f(1) = -20 and f(18) = 219
2.
Write as a single logarithm:
a) 3log x + log (x + 2) - log 4x
b) 2[log (x + 6) - log (x - 2)] + 4log x
3.
Convert from radians to degrees
c) 5π/4
b) 5π/6
a) 7π/3
4.
Convert from degrees to radians
c) 720o
b) 240o
a) 135o
5.
Evaluate (without a calculator)
b) cos 5π/3
a) sin 7π/6
c) tan 5π/4
4
Warm ups.notebook
December 12, 2013
Warm Up
1.
2.
3.
4.
5.
Write a linear equation satisfying the given conditons:
(y + 20) = 239/17(x -1)
f(1) = -20 and f(18) = 219
(y - 219) = 239/17(x - 18)
Write as a single logarithm:
b) 2[log (x + 6) - log (x - 2)] + 4log x
a) 3log x + log (x + 2) - log 4x
log(((x + 6)/(x - 2))2(x4))
log (x3(x + 2)/(4x))
Convert from radians to degrees
c) 5π/4
b) 5π/6
a) 7π/3
O
0
2250
150
420
Convert from degrees to radians
c) 720o
b) 240o
a) 135o
3π/4
4π
4π/3
Evaluate (without a calculator)
c) tan 5π/4
b) cos 5π/3
a) sin 7π/6
-1/√2
1/2
-1/2
5
Warm ups.notebook
December 12, 2013
Warm Up
1.
Write a linear equation satisfying the given conditions:
f(-10) = 3 and f(-40) = -39
2.
Write as a single logarithm:
a) 3log x - .5log (x + 2) - log 2x
3.
b) log (x + 6) + 3log (x - 2) - 5log x
Evaluate (without a calculator)
b) csc 5π/6
a) sec π/2
c) cot 3π/4
d) sin π
e) cos 7π/6
f) tan 4π/3
g) sin 5π/4
h) tan 3π/2
i) cos 5π/6
j) sin 2π/3
6
Warm ups.notebook
December 12, 2013
Warm Up
1.
Write a linear equation satisfying the given conditions:
f(-10) = 3 and f(-40) = -39
(y - 3) = 42/30(x + 10)
(y + 39) = 42/30(x + 40)
2.
Write as a single logarithm:
a) 3log x - .5log (x + 2) - log 2x b) log (x + 6) + 3log (x - 2) - 5log x
log(x3/(2x√(x + 2))
log((x + 6)(x - 2)3/x5)
3.
Evaluate (without a calculator)
b) csc 5π/6 2
a) sec π/2 1/0
d) sin π
0
g) sin 5π/4
-1/√2
c) cot 3π/4 -1
e) cos 7π/6 -√3/2
f) tan 4π/3 √3
h) tan 3π/2 -1/0
i) cos 5π/6 -√3/2
j) sin 2π/3 √3/2
7
Warm ups.notebook
December 12, 2013
Evaluate without using a calculator
Cos (5π/3)
Cot (5π/6)
Sin (3π/2)
Csc (7π/4)
Tan (π)
Sec (3π/4)
8
Warm ups.notebook
December 12, 2013
Evaluate without using a calculator
Cos (5π/3)
Cot (5π/6)
1/2 ­√3
Csc (7π/4)
­√2
Tan (π)
Sin (3π/2)
-1
Sec (3π/4)
0 ­ √2
9
Warm ups.notebook
December 12, 2013
Evaluate without using a calculator
10
Warm ups.notebook
December 12, 2013
Evaluate without using a calculator
11
Warm ups.notebook
December 12, 2013
1. Evaluate without a calculator
a. cos 5π/3
b. sin 7π/4
d. sec 5π/2
e. csc 2π
2. Sketch the graph of:
a. y = 4cos 3(x-π/3) +2
c. tan 7π/6
f. cot 2π/3
b. y = -2sin π(x-2) - 3
3. Write 2 equations (one sin and one cos) for this graph
­2π≤x≤2π
scale is π/2
-5≤y≤5
scale is 1
12
Warm ups.notebook
December 12, 2013
1. Evaluate without a calculator
a. cos 5π/3
b. sin 7π/4
c. tan 7π/6
1/2
-1/√2
1/√3
d. sec 5π/2
e. csc 2π
f. cot 2π/3
-1/0
1/0
-1/√3
2. Sketch the graph of:
a. y = 4cos 3(x-π/3) +2
b. y = -2sin π(x-2) - 3
3. Write 2 equations (one sin and one cos)
for this graph
­2π≤x≤2π
scale is π/2
-5≤y≤5
scale is 1
y = ­2cos 2x +1
y = 2sin 2(x­π/4) + 1
y = 2cos 2(x - π/2) + 1
13
Warm ups.notebook
December 12, 2013
1. Evaluate without a calculator
a. cos 11π/3
b. sin 13π/4
c. tan 7π/6
d. sec 5π/2
f. cot 8π/3
e. csc 4π
2. Sketch the graph of:
a. y = 4cos 3(x-π/3) +2
b. y = -2sin π(x-2) - 3
3. Write 2 equations (one sin and one cos) for this graph
­2π≤x≤2π
scale is π/2
-5≤y≤5
scale is 1
14
Warm ups.notebook
December 12, 2013
1. Evaluate without a calculator
a. cos 11π/3
b. sin 13π/4
c. tan 7π/6
d. sec 5π/2
f. cot 8π/3
e. csc 4π
2. Sketch the graph of:
a. y = 4cos 3(x-π/3) +2
b. y = -2sin π(x-2) - 3
3. Write 2 equations (one sin and one cos) for this graph
­2π≤x≤2π
scale is π/2
-5≤y≤5
scale is 1
15
Warm ups.notebook
December 12, 2013
1. Evaluate without a calculator
a. cos 2π/3
b. sin 3π/2
c. tan 7π/6
d. sec 5π/6
f. cot 3π/4
e. csc π/2
2. Sketch the graph of:
a. y = -2cos 4(x-π/4) +1
b. y = 3sin π(x-5) + 3
3. Write 2 equations (one sin and one cos) for this graph
­π≤x≤π
-10≤y≤10
scale is π/4
scale is 2
16
Warm ups.notebook
December 12, 2013
1. Evaluate without a calculator
a. cos 2π/3
c. tan 7π/6
b. sin 3π/2
-1/2
-1
1/√3
f. cot 3π/4
e. csc π/2
d. sec 5π/6
-2/√3
1
-1
2. Sketch the graph of:
b. y = 3sin π(x-5) + 3
a. y = -2cos 4(x-π/4) +1
3. Write 2 equations (one sin and one cos) for this graph
y = 4cos 4(x) - 2
-π≤x≤π
y = 4sin 4(x+π/8) -2
-10≤y≤10
scale is π/4
scale is 2
y = -4cos 4(x- π/4) - 2
y = -4sin 4(x-π/8) - 2
17
Warm ups.notebook
December 12, 2013
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 18
Warm ups.notebook
1. December 12, 2013
3. 2. 5. 6. ­√3/2
9. 7. -1/√2
-2
8. √3/2
√3
-√3
12. 11. 10. 1
0
­.5
1
4. 0
0
19