Answer: f(120°) = (√3) + 1/2
Step-by-step explanation:
i will solve it with notable relations, because using a calculator is cutting steps.
f(120°) = 2*sin(120°) + cos(120°)
=2*sin(90° + 30°) + cos(90° + 30°)
here we can use the relations
cos(a + b) = cos(a)*cos(b) - sin(a)*sin(b)
sin(a + b) = cos(a)*sin(b) + cos(b)*sin(a)
then we have
f(120°) = 2*( cos(90°)*sin(30°) + cos(30°)*sin(90°)) + cos(90°)*cos(30°) - sin(90°)*sin(30°)
and
cos(90°) = 0
sin(90°) = 1
cos(30°) = (√3)/2
sin(30°) = 1/2
We replace those values in the equation and get:
f(120°) = 2*( 0 + (√3)/2) + 0 + 1/2 = (√3) + 1/2
Answer:
C
Step-by-step explanation:
A major arc is an arc that is greater than 180 degrees.
A minor arc is an arc less than 180 degrees.
An acute angle is an angle less than 90 degrees.
A central angle is the angle created in the center of a circle with 2 sides being the radius.
<em>Thus, we can see in the figure that we are talking about the angle so we can eliminate major arc and minor arc.</em>
<em>Now, we clearly see that the angle is greater than 90 degree so it cannot be acute angle.</em>
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The correct answer is central angle as it goes with the definition.
