Question

Suppose θ is an angle in the first quadrant and cos(θ) = 1/2. What is the value of sin(θ)?

A. 1/2
B. √3/2
C. 3/5
D. -√3/3

Answer 1

B

Explanation:

given

cosΘ =
`(1)/(2)` =
`(adjacent)/(hypotenuse)`

this is a right triangle with hypotenuse = 2 and a leg = 1

using Pythagoras' identity to find the third side o , the opposite side, then

o² + 1² = 2²

o² + 1 = 4 ( subtract 1 from both sides )

o² = 3 ( take square root of both sides )

0 =
`√(3)`

Then

sinΘ =
`(opposite)/(hypotenuse)` =
`(√(3) )/(2)`

Answer 2

B.
`(\sqrt3)/(2)`

Explanation:

Since θ is in the first quadrant, both sin(θ) and cos(θ) are positive.

Using the Pythagorean identity,
`sin^2(θ) + cos^2(θ) = 1`

we can solve for sin(θ) as follows:

`sin^2(θ) + ((1)/(2))^2 = 1`

`sin^2(θ) +(1)/(4)=1`

`sin^2(θ) =1-(1)/(4)`

`sin^2(θ) =(3)/(4)`

`sin(θ) = \sqrt{(3)/(4)} = (\sqrt3)/(2)`

Therefore, the value of sin(θ) is
`(\sqrt3)/(2)`