Unit 1: Trigonometry
Find the missing angle. Round your answer to the nearest degree.
Cos0 = adj/hyp
Adj = 20 Hyp = 23
cos0= 20/23
0= cos-1 (20/23)
0= 30°
What is the probability of rolling doubles with a pair of dice?
P (double) = 6/36
= 1/6
Describe the transformations for y= -11x² + 8
vertical stretched
opens down
shifted 8 units up
vertex (0, 8)
Expand and simplify: (2x + 1) (x + 4)
= 2x (x) + 2x (4) +1 (x) + 1 (4)
= 2x² + 8x + x + 4
= 2x² + 9x + 4
Find the mean, median, and mode: 14, 40, 52, 63, 67, 68, 71, 76, 83, 89, 94, 94, 99
Mean = 910/12 = 70
Median = 71
Mode = 94
Find the angle of elevation. Round to the nearest degree. With the following statements
Tan0= opp/adj
opp= 7 adj= 12
tan0 = 7/12
0= tan-1 (7/12)
0= 30.25
0= 30°
A couple would like to have 3 children. Determine the theoretical probability of having 2 girls and 1 boy.
P (2 girls, 1 boy)= # of outcomes w/ 2 girls/ total # of outcomes
= 3/8
Describe the transformation for y= 0.9 (x+3)²
vertical compression
opens up
shifted 3 units left
vertex (0, -3)
Write in standard form: y= - (x-6)² + 10
y = - (x-6) (x-6) + 10
y= - (x² - 6x - 6x + 36) + 10
y= - (x² - 12x + 36) + 10
y= -x² + 12x - 36 + 10
y= -x² + 12x + 26
Find the median, the first quartile (Q1), and the third quartile (Q3): 6, 7, 13, 17, 20, 25, 39, 41, 43, 49, 51, 62
Median = 25+39/2 = 32
Q1 = 6, 7, 13, 17, 20, 25 = 13 + 17/2 = 15
Q3 = 39, 41, 43, 49, 51, 62 = 43 + 49/2 = 46
Interquartile range = Q3 - Q1 = 46 - 15 = 31
Find the missing angle with the following angles...
51° and 39°
180 - 39 - 51 = 90°
A football quarterback has completed 125 passes in 200 attempts so far in the season. What percent of his passes has he completed?
125/200 = 0.625
0.625 x 100 = 62.5%
Describe the transformations for y= -0.1 (x-6)²
vertical compression
shifted 6 units right
opens down
vertex (6, 0)
Factor the trinomial: x² + 7x - 18
= (x-2) (x+9)
= x² + 9x - 2x - 18
= x² + 7x - 18
Find the mean, median, and mode: 45, 59, 61, 61, 62, 65, 68, 68, 69, 71, 71, 72, 76, 83, 86, 89
Mean = 1106/16 = 69.125
Median = 68 + 69/2 = 68.5
Mode = 61, 68, and 71
Use cosine law to find the missing length of the side
55 cm, 50 cm, and 61°
c² = a² + b² - 2ab x cosc
x² = (55)² + (50)² - 2 (55) (50) cos61
x² = 2858.55
x= √ 2858.55
x= 53.5
During the month of April 2006, at least some rainfall was recorded on 12 different days at the Sarnia Airport weather station. Suppose one day is selected randomly, what is the probability of choosing a day which it rained.
P (rain on selected day) = # of days of rain/ total # of days
= 12/30
= 2/5
= 0.4
= 40%
Describe the transformations for y= 4 (x+7)²
Vertical stretched
Opens up
Shifted 7 units left
Vertex (-7, 0)
Factor the polynomial: 1.2x² - 30
= 1.2 (x² - 25)
=1.2 (x+5) (x-5)
= 1.2 (x² - 5x + 5x - 25)
= 1.2 (x² - 25)
= 1.2x² - 30
Find the mean, median, and mode: 37, 37, 37, 37, 38, 38, 41, 41, 42, 43, 46, 58
Mean = 495/12 = 41.25
Median = 38 + 41/2 = 39.5
Mode = 37
A 10m ladder leans against a wall. The top of the ladder is 9m above the ground. Safety standards call for an angle between the base of the ladder and the ground to be between 70° and 80°. Is the ladder safe to climb?
sin0= opp/hyp
opp= 9m hyp= 10m
sin0= 9/10
0= sin-1 (9/10)
0= 64°
The ladder is safe to climb
A study by Health Canada has shown that, by age 14 1 in 4 teens have tried smoking. Of those who try smoking, 36% become smokers. What is the probability that a person has not tried smoking by age 14?
P (smoking) = 1/4
P (non-smoking) = 3/4
Describe the transformations for y= 0.4x² - 10
Vertical compressed
Opens up
Shifted 10 units up
Vertex (0, -10)
Factor the polynomial: - 4.9t² + 19.6t
= -4.9t (t - 4)
= -4.9t² + 19.6t
Calculate the range, mean, the variance, and the standard deviation: 61, 65, 67, 67, 71, 72, 77, 80, 83, 84, 88, 90
Mean = 905/12 = 75.42 = 75
Range = greatest value - least value = 90 - 61 = 29
Total difference = 1017
Variance = 1017/12 = 85
Standard deviation = √85 = 9