4-6 Solve the equation for θ (0 ≤θ < 2π) . Be careful. There may be several
solutions. Write answers in radians.
4. 2sin^2(θ) =1 5. tan^2(θ) − tan(θ) = 0 7. cos^2(θ) + sin(θ) =1
is the first and second ones just in the 45 degree family?
4-6 Solve the equation for θ (0 ≤θ < 2π) . Be careful. There may be several
solutions. Write answers in radians.
4. 2sin^2(θ) =1 5. tan^2(θ) − tan(θ) = 0 7. cos^2(θ) + sin(θ) =1
is the first and second ones just in the 45 degree family?
Both 1 and 2 consists of the family...
For #1, you get two angles, and another angle. Just keep in mind the quadrants where sine is positive! I'll leave it for you to find the other angle.
However, for #2, we see that we can manipulate the equation a little bit:
We will get two different equations:
and
Keep in mind the restriction on the angle :
Also keep in mind which quadrants tangent is positive!
I hope this helps.
--Chris