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. =)
The answer would be the median because you use the box plot to find the median. its the whole point of a box plot :)
Answer:
48:26.075
Step-by-step explanation:
Answer:
B and D are the correct answers.
Step-by-step explanation:
3) Mathematical expression would be:
412 - 65 + 0.50x
Where, x = Number of Texts sent
4) Product means result after multiplication, sum after addition, quotient is the result of division with remainder, and difference is how far two numbers are in their magnitude.
"Per" tells us the magnitude for an Unit value.
5) Associative property = (a+b) + c = a+ (b+c)
Commutative property = a + b = b + a
Distributive Property = a(b+c) = ab+bc
They all have their unique characteristics and can be differentiated on that basis.
6) They all are same.
At the end, without parentheses and in proper symbol, it would be equal to -3/4
Hope this helps!
