Question

In ΔDFE, which trigonometric ratio has the same value as sin D?

A. cos D
B. tan D
C. cos E
D. sin E

Answer 1

Hello,

sin (30°)= cos (60°)=1/2 (complementary angles)
sin D= cos E

Answer C

Answer 2

C. cos E

Explanation:

We have been given a right triangle DEF. We are asked to find the trigonometric ratio, which has the same value as sin D.

We know that measure of angle F is 90 degrees as all angles of triangle add up-to 180 degrees. The side DE is hypotenuse of triangle DEF.

Let us find sin D for our given triangle.

`\text{Sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}`

`\text{Sin(D)}=\frac{\text{FE}}{\text{DE}}`

We know that cosine relates adjacent side of right triangle to hypotenuse.

`\text{Cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}`

We can see that FE is adjacent side of angle E, so:

`\text{Cos(E)}=\frac{\text{FE}}{\text{DE}}`

Therefore, cos E has the same value as sin D and option 'C' is the correct choice.