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:
h = 9 feet.
Step-by-step explanation:
The height at the top of a roller coaster hill is 10 times the height h feet of the starting point. The height decreases 100 feet from the top to the bottom of the hill. The height at the bottom of the hill is -10 feet.
Therefore, there is a zero elevation point between the starting point at h height and the bottom of the hill which is at - 10 feet from the zero elevation point.
Now, the elevation of the top of the hill from the zero elevation point is (100 - 10) = 90 feet.
Therefore, 10h = 90
⇒ h = 9 feet. (Answer)
Answer:
f(6) = 53
Step-by-step explanation:
f(x) = 10x - 7
We want to find f(6)
To do so simply substitute 6 for x in the equation
Equation: 10x - 7
x = 6
f(6) = 10(6) - 7
multiply 10 and 6
f(6) = 60 - 7
subtract
f(6) = 53
here two given sides are 10 and 6,
We use the rule of triangle here:
sum of two sides> third side
checking for each option
Option A: AC=4
4+6>10, 10>10 (false)
So AC cannot be equal to 4, option A is answer.
