Answer:
- sin = √(1 -cos²)
- tan = (√(1 -cos²))/cos
Step-by-step explanation:
![\displaystyle\sin^2{\theta}+\cos^2{\theta}=1 \qquad\text{Pythagorean identiy}\\\\\sin{\theta}=\sqrt{1-\cos^2{\theta}} \qquad\text{solved for sine}\\\\\tan{\theta}=\frac{\sin{\theta}}{\cos{\theta}}=\frac{\sqrt{1-\cos^2{\theta}}}{\cos{\theta}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csin%5E2%7B%5Ctheta%7D%2B%5Ccos%5E2%7B%5Ctheta%7D%3D1%20%5Cqquad%5Ctext%7BPythagorean%20identiy%7D%5C%5C%5C%5C%5Csin%7B%5Ctheta%7D%3D%5Csqrt%7B1-%5Ccos%5E2%7B%5Ctheta%7D%7D%20%5Cqquad%5Ctext%7Bsolved%20for%20sine%7D%5C%5C%5C%5C%5Ctan%7B%5Ctheta%7D%3D%5Cfrac%7B%5Csin%7B%5Ctheta%7D%7D%7B%5Ccos%7B%5Ctheta%7D%7D%3D%5Cfrac%7B%5Csqrt%7B1-%5Ccos%5E2%7B%5Ctheta%7D%7D%7D%7B%5Ccos%7B%5Ctheta%7D%7D)
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If you draw a triangle with a hypotenuse of 1 and an "adjacent" leg of "cos", then using the Pythagorean theorem, you can see that the "opposite" leg will be √(1-cos²) and the tangent will be (√(1-cos²))/cos. Whether or not you're allowed to draw such a triangle on paper, you can certainly do it in your mind.
Answer:
(3x + 5)(x - 4)
Step-by-step explanation:
Given
x(3x + 5) - 4(3x + 5) ← factor out (3x + 5) from each term
= (3x + 5)(x - 4) ← in factored form
Answer:
24.2
Step-by-step explanation:
37.45-13.25=24.2
24.2/2=12.1
each friend contributes $12.1
Answer:
4
Step-by-step explanation:
PART C:
Another theorem states that in a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. Each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.
This means the ED, a leg of the right triangle, is the geometric mean of EF, the length of the hypotenuse (8) and the EG, the segment adjacent to the leg (2)
ED = Geometric mean =
=
=
= 4
ED = 4