We know that
2π/3 radians-------> convert to degrees-----> 2*180/3---> 120°
120°=90°+30°
Part a) Find <span>sin(2π/3)
</span>sin(2π/3)=sin (90°+30°)
we know that
sin (A+B)=sin A*cos B+cos A*sin B
so
sin (90°+30°)=sin 90*cos 30+cos 90*sin 30
sin 90=1
cos 30=√3/2
cos 90=0
sin 30=1/2
sin (90°+30°)=1*√3/2+0*1/2-----> √3/2
the answer part a) is
sin(2π/3)=√3/2
Part b) Find cos (2π/3)
cos (2π/3)=cos (90°+30°)
we know that
cos (A+B)=cos A*cos B-sin A*sin B
so
cos (90°+30°)=cos 90*cos 30-sin 90*sin 30
sin 90=1
cos 30=√3/2
cos 90=0
sin 30=1/2
cos (90°+30°)=0*√3/2-1*1/2----> -1/2
the answer part b) is
cos (2π/3)=-1/2
Answer:
4.2
Step-by-step explanation:
First I did 54 divided by 3 which is 18. Then I found the square root of 18.
Answer:
<u>Given</u>:
- R(x) = 59x - 0.3x²
- C(x) = 3x + 14
<u>Find the following</u>:
- P(x) = R(x) - C(x) = 59x - 0.3x² - 3x - 14 = -0.3x² + 56x - 14
- R(80) = 59(80) - 0.3(80²) = 2800
- C(80) = 3(80) + 14 = 254
- P(80) = 2800 - 254 = 2546
Approx - 10%
72 students signed up for canoeing + the 23 students who signed up for trekking + the 13 students who signed up for both = 108 students
there are 120 students total, so you have to subtract 120 - 108 = 12
Now to find the percentage, you have to divide the number of students who didn't sign up for either, by the total
which is .1 = 10/100 = 10%
One way to carry out this problem is to simply take the value that you already know, which is that 1/5 is 20 % and multiply it by 2 for 2/5 or 2 (1/5ths) and do this for all of them. There is a pattern that occurs for every increase in one out of denominator of 5.
