The cosine of an angle is the x-coordinate of the point where its terminal ray intersects the unit circle. So, we can draw a line at x=-1/2 and see where it intersects the unit circle. That will tell us possible values of θ/2.
We find that vertical line intersects the unit circle at points where the rays make an angle of ±120° with the positive x-axis. If you consider only positive angles, these angles are 120° = 2π/3 radians, or 240° = 4π/3 radians. Since these are values of θ/2, the corresponding values of θ are double these values.
a) The cosine values repeat every 2π, so the general form of the smallest angle will be
... θ = 2(2π/3 + 2kπ) = 4π/3 + 4kπ
b) Similarly, the values repeat for the larger angle every 2π, so the general form of that is
... θ = 2(4π/3 + 2kπ) = 8π/3 + 4kπ
c) Using these expressions with k=0, 1, 2, we get
... θ = {4π/3, 8π/3, 16π/3, 20π/3, 28π/3, 32π/3}
Answer:
Well that means between the ages of 40 and 60 Bill lost 10 teeth
Step-by-step explanation:
If Bill had 30 teeth when he was 40, and had 20 teeth when he was 60 that means between the ages of 40 and 60 he lost 10 teeth.
Being that 60 minus 40 (60-40=20) is 20, that means he lost 10 teeth in 20 years. Averaging out to loosing 1 tooth every 2 years.
Sorry I was not completely sure what the question was, so I answered it in the most mathematical way possible. Hope I helped a little :)
4.191 to nearest hundred
= 4.19 is your answer
★ Important points to know
- The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
★ Let's solve :-
Hence option A 95⁰ is the right ans ✓