Question

Plz help asap

Use the Pythagorean Identity to find the missing trig function.


a) Find
`sin0` if
`cos0=(1)/(4)`

b) Find
`cos0` if
`sin0=(2)/(5)`

c) Find
`sin0` if
`cos0=(3)/(4)`

Answer 1

Explanation:

a) cos∅=
`(1)/(4)`

√(4²-1²)=√(16-1)=√(15)

∴sin∅=
`(√(15) )/(4)`

b) sin∅=
`(2)/(5)`

√(5²-2²)=√(25-4)=√(21)

∴cos∅=
`(√(21) )/(5)`

c) cos∅=
`(3)/(4)`

√(4²-3²)=√(16-9)=√(7)

∴sin∅=
`(√(7) )/(4)`

Answer 2

Answer:
`\bold{a)\ sin\ \theta=(√(15))/(4)}`

`\bold{b)\ cos\ \theta=(√(21))/(5)}`

`\bold{c)\ sin\ \theta=(\sqrt7)/(4)}`

Explanation:

The Pythagorean Theorem is: a² + b² = c² where;

• a represents adjacent side
• b represents opposite side
• c represents hypotenuse

`a)\ cos\ \theta=(adjacent)/(hypotenuse)=(1)/(4)\\\\1^2+(opposite)^2=4^2\\1 + (opposite)^2=16\\.\ \quad (opposite)^2=15\\.\qquad opposite=√(15)\\\\sin\ \theta = (opposite)/(hypotenuse)=\boxed{(√(15))/(4)}`

`b)\ sin\ \theta=(opposite)/(hypotenuse)=(2)/(5)\\\\(adjacent)^2+2^2=5^2\\(adjacent)^2+4=25\\(adjacent)^2\qquad=21\\adjacent\qquad \ =√(21)\\\\cos\ \theta = (adjacent)/(hypotenuse)=\boxed{(√(21))/(5)}`

`a)\ cos\ \theta=(adjacent)/(hypotenuse)=(3)/(4)\\\\3^2+(opposite)^2=4^2\\9 + (opposite)^2=16\\.\ \quad (opposite)^2=7\\.\qquad opposite=√(7)\\\\sin\ \theta = (opposite)/(hypotenuse)=\boxed{(√(7))/(4)}`