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September 17, 2014

September 17, 2014

Posted by **Bryan** on Friday, November 30, 2007 at 4:27pm.

6. (1 pt) Solve the following equation in the interval [0, 2 p

Note: Give the answer as a multiple of p. Do not use decimal

numbers. The answer should be a fraction or an integer. Note

that p is already included in the answer so you just have to enter

the appropriate multiple. E.g. if the answer is p/2 you should

enter 1/2. If there is more than one answer enter them separated

by commas.

2(cos(t))2−cos(t)−1 = 0

t =________ pi

7. (1 pt) Solve the given equation in the interval [0,2 p].

Note: The answer must be written as a multiple of p. Give exact

answers. Do not use decimal numbers. The answer must

an integer or a fraction. Note that p is already provided with the

answer so you just have to find the appropriate multiple. E.g.

the answer is p

2 you should enter 1/2. If there is more than one

answer write them separated by commas.

2(sin x)2−5cos x+1 = 0

x=__________ pi

- Math (Pre-Calc) -
**Bryan**, Friday, November 30, 2007 at 4:35pmBy the way when is says the interval, it's [0, 2pi] The p's should be pi's

- Math (Pre-Calc) -
**Michael**, Friday, November 30, 2007 at 4:59pmFor the first, factor the equation as you would if cos(t) were x.

For the second, recall that the #1 Identity (most important) is sin^2(x) + cos^2(x) = 1. Solve the identify for sin^2(x) and plug that into your equation so that it contains*only*cosine. Then, factor the equation as you would if cos(x) were simply x.

Try that, and if you have any problems, let us know.

- Math (Pre-Calc) -
**Bryan**, Friday, November 30, 2007 at 5:55pmSo for the first the answers would be pi/3, pi, 5pi/3?

I tried it for the second problem and I couldn't make it work.

- Math (Pre-Calc) -
**Bryan**, Friday, November 30, 2007 at 6:04pmnever mind...I got the first problem figured out. The second is still stumping me however.

- Math (Pre-Calc) -
**Michael**, Friday, November 30, 2007 at 9:14pmStart by solving the #1 Identity: sin^2(x) + cos^2(x) = 1 for sin^2(x)...

sin^2(x) = 1 - cos^2(x)

Our equation is 2(sinx)^2 − 5cos(x) + 1 = 0

(sinx)^2 is the same as sin^2(x), so replace it with 1 - cos^2(x)...

2(1 - cos^2(x)) - 5cos(x) + 1 = 0

Distribute in the 2 and simplify. Then, factor.

- Math (Pre-Calc) -

- Math (Pre-Calc) -

- Math (Pre-Calc) -

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