5
If tan θ = —— , calculate the value of cos θ:
4
Recall the definition of the tangent function:
sin θ
tan θ = ————
cos θ
5 sin θ
—— = ————
4 cos θ
Cross multiply:
5 · cos θ = 4 · sin θ
Square both sides:
(5 · cos θ)² = (4 · sin θ)²
5² · cos² θ = 4² · sin² θ
25 · cos² θ = 16 · sin² θ
But sin² θ = 1 – cos² θ. Substitute that for sin² θ into the equation above, then you get
25 · cos² θ = 16 · (1 – cos² θ)
25 · cos² θ = 16 – 16 · cos² θ
Isolate cos² θ:
25 · cos² θ + 16 · cos² θ = 16
(25 + 16) · cos² θ = 16
41 · cos² θ = 16
16
cos² θ = ———
41
4²
cos² θ = ————
(√41)²
Take square root of both sides:
4
cos θ = ± ———
√41
4 4
cos θ = – ——— or cos θ = ——— ✔
√41 √41
The sign of cos θ depends on which quadrant θ lies. Since you first have a positive value for tan θ, then that means θ lies either in the 1st or the 3rd quadrant.
• If θ is a 1st quadrant angle, then
cos θ > 0
4
cos θ = ——— ✔
√41
• If θ is a 3rd quadrant angle, then
cos θ < 0
4
cos θ = – ——— ✔
√41
I hope this helps. =)
Answer:
70 cars per year.
Step-by-step explanation:
Given:
In 1984 a locally-owned car company sold 2,743 cars.
In 2003, the car sales rose to 4,069.
Question asked:
What was the average rate of change for the total number of cars sold?
Solution:
In 2003 number of cars sold = 4069
In 1984 number of cars sold = 2743
Change in the number of car sold = 4069 - 2743
= 1326
Now, time interval between 2003 and 1984 = 19
Thus, the average rate of change for the total number of cars sold is 70 cars per year.
The equations are y=3x-1 and y=-3x+5
I’ll try to solve it in the comments if you still have time
Given that, a bike wheel is 26 inches in diameter.
We need to convert bike wheel's diameter in millimeters .
Since, 1 inch = 25.4 millimeters.
So, to convert 26 into mm we need to multiply 26 each sides of this identity to convert this into mm. Hence,
1*26 inch = 25.4 * 26 mm.
So, 26 inches = 660.4 mm.
So, the bike wheel's diameter is 660.4 millimeters.
Hope this helps you!
Answer:
15.3
Step-by-step explanation:
18-(18×(15%))= 15.3
