Question

Choose the correct value of sin theta if cos theta=4/5 answer

Answer 1

Step-by-step explanation:

follow the above steps

Answer 2

Concept

In a Right-angled triangle, sinФ is defined as the ratio of the opposite side to the hypotenuse of the triangle.

The cosФ is the ratio of the adjacent side to the hypotenuse.

Given

cosФ = 4/5

Find

Value of sinФ

Solution

We have 2 ways of solving

Method 1

We know that

sin2Ф + cos2Ф = 1

sin2Ф = 1 - cos2Ф................(1)

Calculating cos2Ф

cos2Ф = cosФ * cosФ

cos2Ф = 4/5 * 4/5

cos2Ф = 16/25

Putting value of cos2Ф in (1)

sin2Ф = 1 - 16/25

sin2Ф = (25-16)/25

sin2Ф = 9/25

sinФ = 3/5 and -3/5

Method 2

Using Triangle

We have a  right angled triangle with hypotenuse as 5 , base as 4 and altitude as 3.

cosФ = b/h = 4/5

sinФ = altitude/hypo = 3/5

The correct value of sinФ is 3/5 and -3/5 if sinФ lies in I Quadrant and IV Quadrant respectively.

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