Question

If sin0 = 3/4 and is in the first quadrant, then cos0 =

a. 4/5
b. (sqrt 7)/4
c. 1/4
d. (sqrt 21)/3

Answer 1

`\displaystyle b) { ( \sqrt7)/( 4) }`

Explanation:

we are given that

`\displaystyle \sin( \theta) = (3)/(4)`

we want to figure out Cos
`\theta`

in order to do so we can consider Pythagoras trig indentity given by

`\displaystyle \cos ^(2) ( \theta) = 1 - { \sin}^(2) ( \theta)`

given that,sin
`\theta`=¾

thus substitute,

`\displaystyle \cos ^(2) ( \theta) = 1 - \bigg({ (3)/(4) } \bigg)^(2)`

simplify square:

`\displaystyle \cos ^(2) ( \theta) = 1 - { (3 ^(2) )/(4 ^(2) ) }`

`\displaystyle \cos ^(2) ( \theta) = 1 - { (9 )/(16 ) }`

simplify substraction:

`\displaystyle \cos ^(2) ( \theta) = { (16- 9)/(16 ) }`

`\displaystyle \cos ^(2) ( \theta) = { (7)/(16 ) }`

square root both sides:

`\displaystyle \sqrt{\cos ^(2) ( \theta) }= \sqrt{{ (7)/(16 ) } }`

By square root property:

`\displaystyle \cos ^{} ( \theta) = { ( \sqrt7)/( √(16 )) }`

simplify root:

`\displaystyle \cos ^{} ( \theta) = { ( \sqrt7)/( 4) }`

hence, our answer is b

Answer 2

`\sin(θ) = (p)/(h) = (3)/(4)`

so

p=3

h=4

b=
`\sqrt{4 {}^(2) - {3}^(2) }`

b=
`√(7)`

Now

cosθ=
`(b)/(h) = ( √(7) )/(4)`

So

b.
`( √(7) )/(4)` is a required answer.