Use following substitutions:
<span>r cosθ = x </span>
<span>r sinθ = u </span>
<span>r² = x² + y² </span>
<span>r = 8 cosθ + 4 sinθ </span>
<span>Multiply both sides by r </span>
<span>r² = 8 r cosθ + 4 r sinθ </span>
<span>x² + y² = 8x + 4y </span>
<span>This is equation of circle. We can put in standard form: </span>
<span>x² − 8x + y² − 4y = 0 </span>
<span>x² − 8x + 16 + y² − 4y + 4 = 16 + 4 </span>
<span>(x − 4)² + (y − 2)² = 20 </span>
<span>Circle centered at point (4, 2) with radius = √20</span><span />
Answer:
3/12 0.146 0.279 5/7
Step-by-step explanation:
3/12 = 0.25
5/7 = 0.71428571428
Answer: In the exact order up to down: 80, 74, 110, 96, 80
Step-by-step explanation:
Do the equation
360=(x-6)+(x+30)+1.2x+x
we can simplify by doing
360=(x-6)+(x+30)+2.2x
=360=x-6+x+30+2.2x
=360=4.2x+24
=336=4.2x
=80=x
x=80
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A) cos a = (√22)/5; tan a = (√66)/22
B) sin a = (2√2)/3; tan a = 2√2
C) sin a = (√30)/6; cos a = (√6)/6
D) sin a = 3/5; tan a = 3/4
E) sin a = (5√26)/26; cos a = (√26)/26
F) sin a = 3/5; tan a = 3/4
Explanation
The ratio for sine is opposite/hypotenuse. This means the side opposite the angle is √3 and the hypotenuse is 5. Using the Pythagorean theorem to find the adjacent side,
(√3)² + A² = 5²
3+A² = 25
A² = 22
A=√22
This means that cos a = adjacent/hypotenuse = (√22)/5 and tan a = opposite/adjacent = (√3)/(√22) = (√66)/22.
B) The ratio for cosine is adjacent/hypotenuse; this means the side adjacent to the angle is 1 and the hypotenuse is 3. Using the Pythagorean theorem to find the side opposite the angle (p),
1² + p² = 3²
1+p² = 9
p² = 8
p=√8 = 2√2
This means that sin a = opposite/hypotenuse = (2√2)/3 and tan a = opposite/adjacent = (2√2)/1 = 2√2.
C) The ratio for tangent is opposite/adjacent; this means that the side opposite the angle is √5 and the side adjacent the angle is 1. Using the Pythagorean theorem to find the hypotenuse,
(√5)²+1² = H²
5+1=H²
6=H²
√6 = H
This means that sin a = opposite/hypotenuse = (√5)/(√6) = (√30)/6 and cos a = adjacent/hypotenuse = 1/(√6) = (√6)/6.
D) The ratio for cosine is adjacent/hypotenuse; this means that the side adjacent the angle is 4 and the hypotenuse is 5. Using the Pythagorean theorem to find the side opposite the angle, p:
4²+p²=5²
16+p²=25
p²=9
p=3
This means that sin a = opposite/hypotenuse = 3/5 and tan a = opposite/adjacent = 3/4.
E) The ratio for tangent is opposite/adjacent;; this means that the side opposite the angle is 5 and the side adjacent the angle is 1. Using the Pythagorean theorem to find the hypotenuse,
5²+1²=H²
25+1=H²
26=H²
√26 = H
This means that sin a = opposite/hypotenuse = 5/(√26) = (5√26)/26 and cos a = adjacent/hypotenuse = 1/(√26) = √26/26.
F) 0.8 = 8/10; The ratio for cosine is adjacent/hypotenuse. This means that the side adjacent the angle is 8 and the hypotenuse is 10. Using the Pythagorean theorem to find the side opposite the angle, p:
8²+p² = 10²
64+p² = 100
p² = 36
p=6
This means that sin a = opposite/hypotenuse = 6/10 = 3/5 and tan a = opposite/adjacent = 6/8 = 3/4.
Answer:A is the correct answer
Step-by-step explanation:
