Fatima wants to find the value of sin 0 given cot 0 = 4/7 which identity should she use

Remark

The cot (theta) = 4/7

That means we have an adjacent of 4 and an opposite of 7. We still need to find the hypotenuse.

Step One

Find the hypotenuse

a^2 + b^2 = c^2

a = 4

b = 7

c = ?

4^2 + 7^2 = c^2

c^2 = 16 + 49

c^2 = 65 Take the square root of both sides.

c = sqrt (65)

Now find Sin (theta)

Sin (theta) = 7 / sqrt (65)

The other way to do it would be to solve

cot^2 (theta) + 1 = csc^2 (theta)

(4/7) ^2 + 1 = csc^2 (theta)

16/49 + 1 = csc^2 (theta)

65/49 = csc^2 (theta)

sqrt (65) / 7 = csc (theta)

7 / sqrt (65) = sin (theta)

There's a choice of two ways to do it. The first way is using cot = adjacent / opposite.

The second is using

1 + cot^2 (theta) = csc^2 (theta) and

sin (theta) = 1 / csc (theta).