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. =)
A=Lw
The area is 12*34, 408 sq ft.
The best way to find out what 7 sweets cost, firstly, you should find out what one sweet would cost. You have 5 sweets, with a total cost of 30p. You should divide 30 by 5, giving you 6p per sweet. To get the cost of 7 sweets, you have to multiply 6p by 7, giving you 42p.
Therefore, the cost of 7 sweets is 42p.
Hope this helps :)
10.36 and you will get 19.30
Answer:
you have a cubic function right? what are you trying to do?? find intercepts?? need a little more information
