1. ## angles

Dad gave me about 50 problems to sharpen my skills for the up coming school year...

1. Find the period of the graph of the equation y=2sin(pi x-3)

2. Find all solutions to the equation cos x=-1

choices

a. x= pi n
b. x= 2pi n
c. x= pi/2+ pi n
d. x= pi + 2 pi n

3. Use the addition and subtraction formula to simplify cos(x+pi)

Ya'll are great thanks

2. Hello, ccdalamp!

3. Use the addition and subtraction formula to simplify $\displaystyle \cos(x+\pi)$
We're expected to know: .$\displaystyle \cos(A \pm B) \;=\;\cos(A)\cos(B) \mp \sin(A)\sin(B)$

We have: .$\displaystyle \cos(x + \pi) \;=\;\cos(x)\cos(\pi) - \sin(x)\sin(\pi)$

We're also expected to know that: .$\displaystyle \cos(\pi) = -1$ .and .$\displaystyle \sin(\pi) = 0$

Therefore, we have: .$\displaystyle \cos(x)\!\cdot\!(-1) - \sin(x)\!\cdot\!(0) \;=\;-\cos(x)$

3. Originally Posted by ccdalamp
Dad gave me about 50 problems to sharpen my skills for the up coming school year...

1. Find the period of the graph of the equation y=2sin(pi x-3)
see my first post here

2. Find all solutions to the equation cos x=-1

choices

a. x= pi n
b. x= 2pi n
c. x= pi/2+ pi n
d. x= pi + 2 pi n
the cosine function hits -1 once in every period. so if we can find one instance where it hits -1, in say, $\displaystyle 0 \leq x \leq 2 \pi$ for x in radians, we can just supplement that by adding some constant times $\displaystyle 2 \pi$ to get the value for any other period, since all the -1
s will be a period apart (which is $\displaystyle 2 \pi$ for cos(x))

cos(x) = -1 when x = pi in the period [0,2pi]

thus all solutions can be given by: $\displaystyle x = \pi + 2n \pi$ for $\displaystyle n$ an integer. which is choice d