Blog Final Problems

3.Simplify and find the sum.

10
∑ 2+(n-1)5
n=1


10
∑5n - ∑3
n=1

10
5∑n - ∑3
n=1


5(11)(5) - 30


275 - 30 = 45


5. Find sin of a 30 degree angle.

Y= 1, X= √3, R = 2

Sin= Y/r, so sin= 1/2


6. Convert 45 degrees in radians.

450 degrees * л/180 degrees = 2.5л or 5л/2



7. Find all first revolution angles if cot= 3/5

cot=x/y, tan=y/x

tan= 5/3, then you get its inverse.

so the angle= tan-1 (5/3)

angle= 59.03, 239.04



8.Find the recusrive and explcit definition for the sequence 2,4,6,8,10. Then find T20.

2,4,6,8,10

2 2 2 2

t1=2, d=2

Explicit= T1 + (n-1)d

= 2+ (n-1)d

= 2n



Recursive= T1=2

Tn=T(n-1) +2



T20 = 2(20)

t20 = 40



9. Find the sum of 2,1,0.5,0.25,0.125

1/2 = 0.5, 0.5/1 = 0/5

Rate = 0.5

Sn=t1/1-r, Sn= 2/0.5

Sum =4



10.Find 5 trig functions if cot=3/4 in the 1st quadrant.

Cot=x/y, so y=4 and x=3

Using pythagorean theorem, find r.

3^2+4^2=r^2

9+16=r^2

25=r^2

√25=r

5=r
sin=y/r or 4/5

cos=x/r or 3/5

tan=y/x or 4/3

sec=r/x or 5/3

csc=r/y or 5/4

11. Solve for 2sin -9 =3

2sin = 12

sin = 6

Since sin = y/r, and y cant be greater than the radius, this is undefined.

12.A circle has a radius of 30cm. Find the sector of a 30 degree angle.
s=r * angle

convert the angle in radians

30 degree * π/180 degrees = π/6

π/6 * 30cm = 15.7 cm

14. Find the sum of 1 + 3 + 5+ 7+ 9+ ..t15 using sigma notation.

difference= 2
t1=1
Explicit formula = 1 + (n-1)2
= 2n-1

8
∑ 2n-1
n=1

8
∑2n - ∑1
n=1

8
2∑n - 8
n=1

72-8 = 64