### sin (a + b) = sin (a) * cos

```MCB3 group; Homework due on 03-25-2017
(1)
sin (a + b) = sin (a) * cos (b) + sin (b) * cos (a)
- this equation is
always true; it is a fundamental formula, and we will prove it sometime.
T1
Based on the identity (1) prove the following identities
sin (a - b) = sin (a) * cos (b) - sin (b) * cos (a)
We did this in the class; make sure you understand the way we use
the fact that sin(a) is an odd function and cos(a) is an even function.
We also use the definition of subtraction (it is addition of opposite).
T2
Using formula (1) prove identity
(Hint: in formula (1) set b = a)
--------------
T3
sin (2*a) = 2 * sin(a) * cos(a)
Solve equation: sin (x) = sin (2*x) , if 0
≤
x
≤
2* π
T4
If 0
≤
x
≤
π;
cos(x) = 3/5; how much is sin(2*x)
T5
If sin(35°) = K, then how much is sin (70°), and cos (70°) in terms of K?
T6*
sin (2*t) = 24/25; and
How much is cos (t)?
T7
Prove identity
T8
Prove identity
0
< x
<
π/2 ;
T9*
Compute
Q1
Nick read 100 pages at the rate of 50 pages an hour in the morning; in the evening he
was reading 100 pages at the rate 40 pages per hour. What was his average for reading
per hour for the whole day?
Q2
A farmer had to plough the field in 5 days. However, he increased his productivity by 2
acres a day, and finished the job 1 day earlier than planned. What is the area of his field
in acres?
Q3
Graph of equation x2 + y2 = 169 is a circle. Which of the following points is outside
the circle?
A)
B)
C)
D)
E)
(5, 12)
(9, 9)
(11, 5)
(10, 10)
None of the above.
Solve inequalities
I1
-x2 + 12*x + 28
I2
3 / (x + 3)
I3
x42
>
<
9 * x45
1/3
> 0
```