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
Answer:
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Answer:
Step-by-step explanation:
in y = mx + b form, the slope is in the m position and the y intercept is in the b position.
y = mx + b
slope(m) = 5/7
y int (b) = -3
y = 5/7x - 3 <===
1. For x<3, h(x)=x+2
now x+2 is an increasing line (a practical way to check, h(1)=3, h(2)=4)
the largest value it takes is at 3, not inclusive, so h(3)=5 not inclusive.
Range_1= (-∞, 5)
2. for x> or equal to 3, h(x)=-x+8, which is a decreasing line (check h(4)=4, h(5)=3 )
so this line takes its maximal value at x=3, f(3)=5 and then takes any other value to -∞.
Range_2=(-∞,5]
3. Range(h)=Range1∪Range2=(-∞, 5)∪(-∞,5]=(-∞,5] (B)
Step-by-step explanation:
One fish eats = 4 pellets
Second fish eats = 5 pellets
No of days one fish stays with Sophie = 72 ÷ 4 = 18 days
No of days second fish stays with Sophie = 72 ÷ 5 = 14.4 days
