given that cos 0=7/8 qnd the angle 0 is in the first quadrant, find the value for sin 0.

Answer 1

If we draw a triangle out, we know that cos x = adjacent/hypotenuse.

Cos 0 = 7/8 so we know that...

Adjacent = 7 and

Hypotenuse = 8

We now need to find the opposite side to angle 0. We can do this using the Pythagorean Theorem.

a²+b²=c²

Let's use our adjacent for a (since it can be either a or c) and our hypotenuse for c (since c has to be the hypotenuse).

7²+b²=8²

When we simplify it looks like

49+b²=64

We need to isolate the variable.

b²=15

b=√15

We now know...

Adjacent = 7,

Opposite = √15, and

Hypotenuse = 8

Sin x = opposite/hypotenuse.

Sin 0 = √15/8