Given that sinθ = a/b, then cosθ is equal to
a. b/√(b²-a²)
b. a/√(b²-a²)
c. √(b²-a²)/b
d. b/a

Solution:

Given, sinθ = a/b

We have to find the value of cosθ.

We know that sin A = opposite/hypotenuse

Opposite = a

Hypotenuse = b

Using the pythagorean theorem,

(hypotenuse)² = (opposite)² + (adjacent)²

(b)² = (adjacent)² + (a)²

(adjacent)² = b² - a²

Taking square root,

Adjacent = √(b² - a²)

We know that cos A = adjacent / hypotenuse

cosθ = √(b² - a²)/b

Therefore, the value of cosθ is √(b² - a²)/b.

✦ Try This: Given that sinθ = x/y, then tanθ is equal to

Given, sinθ = x/y

We have to find the value of tanθ.

We know that sin A = opposite/hypotenuse

Opposite = x

Hypotenuse = y

Using the pythagorean theorem,

(hypotenuse)² = (opposite)² + (adjacent)²

(y)² = (adjacent)² + (x)²

(adjacent)² = y² - x²

Taking square root,

Adjacent = √(y² - x²)

We know that tan A = opposite/adjacent

tanθ = x/√(y² - x²)

Therefore, the value of tanθ is x/√(y² - x²)

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8

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NCERT Exemplar Class 10 Maths Exercise 8.1 Problem 4

Given that sinθ = a/b, then cosθ is equal to a. b/√(b²-a²), b. a/√(b²-a²), c. √(b²-a²)/b, d. b/a

Summary:

The cosine function can be defined as the ratio of the length of the base to the length of the hypotenuse in a right-angled triangle.Given that sinθ = a/b, then cosθ is equal to √(b²-a²)/b

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☛ Related Questions:

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