Question

What value of θ makes sinθ = cos30° a true statement? A) 30° B) 45° C) 60° D) 90°

Answer 1

Answer:

Step-by-step explanation:

d

Answer 2

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

Step-by-step explanation :

As we know that:

$\cos 30^o=\frac{\sqrt{3}}{2}$     ........(1)

According to trigonometric function,

$\cos \theta=\frac{Base}{Hypotenuse}$     .........(2)

By comparing 1 and 2, we can say that:

$\cos 30^o=\frac{\sqrt{3}}{2}=\frac{Base}{Hypotenuse}$

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

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

$(2)^2=(Perpendicular)^2+(\sqrt{3})^2$

$4=(Perpendicular)^2+3$

$(Perpendicular)^2=4-3$

$(Perpendicular)^2=1$

$Perpendicular=1$

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

According to trigonometric function,

$\sin \theta=\frac{Perpendicular}{Hypotenuse}$

$\sin \theta=\frac{1}{2}$

At $\theta =30^o$

$\sin 30^o=\frac{1}{2}$

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