Answer:
A) sin θ = 3/5
B) tan θ = 3/4
C) csc θ = 5/3
D) sec θ = 5/4
E) cot θ = 4/3
Step-by-step explanation:
We are told that cos θ = 4/5
That θ is the acute angle of a right angle triangle.
To find the remaining trigonometric functions for angle θ, we need to find the 3rd side of the triangle.
Now, the identity cos θ means adjacent/hypotenuse.
Thus, adjacent side = 4
Hypotenuse = 5
Using pythagoras theorem, we can find the third side which is called opposite;
Opposite = √(5² - 4²)
Opposite = √(25 - 16)
Opposite = √9
Opposite = 3
A) sin θ
Trigonometric ratio for sin θ is opposite/hypotenuse. Thus;
sin θ = 3/5
B) tan θ
Trigonometric ratio for tan θ is opposite/adjacent. Thus;
tan θ = 3/4
C) csc θ
Trigonometric ratio for csc θ is 1/sin θ. Thus;
csc θ = 1/(3/5)
csc θ = 5/3
D) sec θ
Trigonometric ratio for sec θ is 1/cos θ. Thus;
sec θ = 1/(4/5)
sec θ = 5/4
E) cot θ
Trigonometric ratio for cot θ is 1/tan θ. Thus;
cot θ = 1/(3/4)
cot θ = 4/3
it says i need to have at least 20 characters so here you go buddy
The answers are :
10) 25 : 24
11) 24 : 5
12) 36 : 5
13) 7 : 3
14) 15 : 1
<u>Ratio = Number of event 1 : Number of event 2</u> (in same unit, if necessary)
<u>10</u>
Girls preferring orange juice : Boys preferring orange juice
50 : 48 (Divide by 2 on both sides)
25 : 24
<u>11</u>
Boys preferring orange juice : Boys preferring grapefruit juice
48 : 10 (Divide by 2 on both sides)
24 : 5
Remember :
- <u>1 minute = 60 seconds</u>
- <u>1 week = 7 days</u>
- <u>1 hour = 60 minutes</u>
<u />
<u>12</u>
3 minutes : 25 seconds
3 × 60 : 25 (Divide by 5 on both sides)
3 × 12 : 5
36 : 5
<u>13</u>
2 weeks : 6 days
2 × 7 : 6 (Divide by 2 on both sides)
7 : 3
<u>14</u>
5 hours : 20 minutes
5 × 60 : 20 (Divide by 20 on both sides)
5 × 3 : 1
15 : 1
(slope) The higher the gradient<span> of a graph at a point, the steeper the </span>line<span> is at that point.</span>
36.
Convert 10% to .1, (10 divided by 100)
then multiply 40 times .1
then subtract 4 by 40
=36
