Lalas and Susy Lecs. Final assignment

3. Given a series written in Sigma Notation simplify and evaluate.

15
∑5 (0.59) ^n-1
K=1

T1=5 Sn= 5(1-(0.5) ^15)
R=0.5 (1-0.5)


Sn≈ 9.999



5. Find the exact value of any trig function for any special angle. ( no calc)

Find Sec of a 45 degree angle.






Sec= r/x
Sec= √2

6. Convert between degrees and radians.

Convert -90 degrees in radians.

360-90=270 degrees

270x Л = 3 Л
180 2



7. Find all 1st revolution angles that have a given value for one of the 6 trig functions.

Find all 1st revolution angles for Sec= 4/2

Sec=4/2 Cos= 1
4/2
Cosθ^cos -1 = 2/4
θ= Cos^-1(1/2)
θ=60 degrees, 30 degrees

8.Write and use recursive and explicit definitions of sequences.

Find recursive and explicit definition for 3,12,48. Them find T10

T1=3 12/3=4 48/12=4

Explicit= T1•r^(n-1)

T10=3(4)^9
T10=786,432

Recursive: T1=3
Tn=Tn-1.4

9. Find the Sum of Finite and Infinite geometric and arithmetic series.
Find the sum of 3+6+9+12+15+18 find t6

t1= 3 n●(t1 + tn)/2 3(3+18)= S6 S6=63
d= 3

10. Given the value of any one of the 6 trig functions and a quadrant for the angle, find values for the other 5 trig functions.
Find 5 trig functions if sinθ 3/5 in the second quadrant
Y=3; X=4; R=5
x^2+y^2=r^2
x^2= r^2-y^2 cosθ= 4/5, tanθ=3/4, cotθ=4/3, cscθ=5/3, secθ=5/4
x^2­=5^2-3^2
x^2=25-9
x^2=16
x=4




11. Solve trigonometric equations
Solve for all revolution angles if sinθ-3=4 sinθ-3+3=4+3 sinθ/2=7(2) sinθ=14 θ= undefined

12. Solve Sector, arc lengh, central angle, radius problems
The sector of a 40° angle is 4cm find the radius 40° (Л/180) = 0.222Л= 0.698131 s/θ= rθ/θ s/θ=r 4cm/0.698=r r= 5.729cm

13. solve word problems involving sequences and series
Find the sum of 2+4+6+8+10 using sigma
5 5d=2 Σ2n= 2Σn 5/2= (6)(2)= 30t1=2 n=1 n=1