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:
<u>True</u>
Step-by-step explanation:
3³ x 4
= 3 x 3 x 3 x 4
= 9 x 12
= 108
<u>True</u>
m =(y2-y1)/(x2-x1)
m =(-2 + 3 )/(-3 -2)
m = 1/-5
m = -1/5
slope of the line that is perpendicular = 5
Answer:
your sister would be 35
Step-by-step explanation:
