math
posted by raj .
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

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.

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
Respond to this Question
Similar Questions

Trig  Identies/equation, please help!
2Sin(Θ+47°)=1 ΘЄ[0°, 360°) What I did: Sin(Θ+47°)=1/2 Sin 1/2 = Θ+47° 30°+360 = Θ+47° 343° = Θ Ok, so how do i find the other solutions? 
MathTrig
Trig Questions 1. Write the algebraic expression which shows Cos((ArcSin(4/X)), 2. Angle If Csc(Θ)=15/4? 
mathTrig
1. Write the algebraic expression which shows Cos((ArcSin(4/X)), 2. Angle If Csc(Θ)=15/4? 
Trigonometry
1. Find the exact value of the following (Think identity) Cos(2 Arccos(5/13)) 2. Solve the following equation for 0° ≤ Θ < 360° Sec(Θ)= tan(Θ) + cos(Θ) 
TRIGONOMETRY HELP
Prove that: (tan²Θ)x(sin²Θ) = (tan²Θ)(sin²Θ) show work 
TRIGONOMETRY HELP
Prove that: cos²Θ  sin²Θ = 2cos²Θ  1 
please
Given tan Θ =  8/5 and sin Θ < 0, find sin Θ, cos Θ, csc Θ, sec Θ and cot Θ. 
Probability
Let Θ1 and Θ2 be some unobserved Bernoulli random variables and let X be an observation. Conditional on X=x, the posterior joint PMF of Θ1 and Θ2 is given by pΘ1,Θ2∣X(θ1,θ2∣x)= 0.26, … 
calc 2
Consider the 4 leaf rose and a circle having polar equations: r=10cos(2Θ) and r=5 with 0≤Θ≤2π, respectively. Find the area of the region that lies inside the rose and outside the circle. hint: find the smallest … 
PreCalculus
This question has me stuck. Use the Pythagorean identity sin^2 Θ + cos^2 Θ = 1 to derive the other Pythagorean identities, 1 + tan^2 Θ = sec^2 Θ and 1 + cot^2 Θ = csc^2 Θ. Discuss how to remember these …