First way
arcsin(1/4) means that 1/4 sin of the angle.
sin(α)=1/4
sin²α+cos²α=1
(1/4)²+cos²α=1
cos²α=1-1/16 =15/16
cosα=+/-(√15)/4
<span>Second way
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sin(α)=1/4 =opposite leg/hipotenuse
cos(α)=adjacent leg/hypothenuse
adjacent leg =√(hypotenuse²- Opposite²)=√(16-1)=√15
cosα=+/-√15/4
For one value of sinα, possible 2 values of cosα.
Answer:
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If you look in a table of sines, you find that sin(θ) = 0.45 corresponds to an angle of about 26°45', so is nearest to 27°.
Answer:
We can set up a system of equations.
x + y = 111
0.25x + 0.10y = 18.30
x + y = 111
Subtract 'y' to both sides:
x = -y + 111
Plug in '-y + 111' for 'x' in the 2nd equation:
0.25(-y + 111) + 0.10y = 18.30
Distribute 0.25 into the parenthesis:
-0.25y + 27.75 + 0.10y = 18.30
Combine like terms:
-0.15y + 27.75 = 18.30
Subtract 27.75 to both sides:
-0.15y = -9.45
Divide -0.15 to both sides:
y = 63
Plug this back into any of the two equations to find the 'x' value.
x + y = 111
x + 63 = 111
Subtract 63 to both sides:
x = 48
So there are 48 quarters and 63 dimes.
Step-by-step explanation:
Hope This Helps!
