Question

What value of θ makes sinθ = cos30° a true statement?

A) 30°
B) 45°
C) 60°
D) 90°

Answer 1

Explanation:

d

Answer 2

Answer : The correct option is, (A) 30°

Step-by-step explanation :

As we know that:

`\cos 30^o=(√(3))/(2)` ........(1)

According to trigonometric function,

`\cos \theta=(Base)/(Hypotenuse)` .........(2)

By comparing 1 and 2, we can say that:

`\cos 30^o=(√(3))/(2)=(Base)/(Hypotenuse)`

Now we have to determine the value of perpendicular by using Pythagoras theorem.

`(Hypotenus)^2=(Perpendicular)^2+(Base)^2`

`(2)^2=(Perpendicular)^2+(√(3))^2`

`4=(Perpendicular)^2+3`

`(Perpendicular)^2=4-3`

`(Perpendicular)^2=1`

`Perpendicular=1`

Now we have to determine the value of
`\sin \theta`.

According to trigonometric function,

`\sin \theta=(Perpendicular)/(Hypotenuse)`

`\sin \theta=(1)/(2)`

At
`\theta =30^o`

`\sin 30^o=(1)/(2)`

Hence, the value of
`\theta` is
`30^o`