Posted by **raj** on Monday, October 29, 2007 at 10:50am.

Solve the following equations giving any roots in terms of pi in the .......?

interval -2pi ≤ 0 ≤ 2pi.

a) 2cos²Θ + sin²Θ = 0

b) 2cos²Θ + sin²Θ = 1

c) 2cos²Θ + sin²Θ = 2

- math -
**drwls**, Monday, October 29, 2007 at 12:16pm
First convert cos^2 theta to 1 - sin^2 theta. Then treat sin^2 as a new variable x and solve for that using quadratic equation procedures.

- math -
**Reiny**, Monday, October 29, 2007 at 1:45pm
I will do the last one for you

2cos²Θ + sin²Θ = 2

2cos²Θ + 1 - cos²Θ = 2

cos²Θ = 1

cosΘ = ±1

in degrees, Θ = 0º or 180º or 360º

in radians: Θ = 0 pi or 2pi

## Answer this Question

## Related Questions

- please - Given tan Θ = - 8/5 and sin Θ < 0, find sin Θ, cos &#...
- math-Trig - 1. Write the algebraic expression which shows Cos((ArcSin(4/X)), 2...
- TRIGONOMETRY HELP - Prove that: cos²Θ - sin²Θ = 2cos²Θ - 1
- Math-Trig - Trig Questions- 1. Write the algebraic expression which shows Cos((...
- Trig - Identies/equation, please help! - 2Sin(Θ+47°)=1 ΘЄ[0°, ...
- Trigonometry - 1. Find the exact value of the following (Think identity) Cos(2 ...
- probability - Theoretical properties Let Θˆ be an estimator of a random ...
- Probability - Let Θ1 and Θ2 be some unobserved Bernoulli random ...
- TRIGONOMETRY HELP - Prove that: (tan²Θ)x(sin²Θ) = (tan²Θ)-(sin²&#...
- Probability - The random variable X is uniformly distributed over the interval...