If sin θ = 1/2 and angle θ is acute, how do you find the other five ratios?

Solution:

Given,

sin θ = 1/2.

angle θ is acute.

So, sin θ lies in the 1st quadrant. This makes all the values positive.

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

cos²θ = 1 -sin²θ = 1 - 1/4 = 3/4.

cosθ = √3/2.

tanθ = sinθ /cosθ = 1/2 / √3/2 =1/√3.

cotθ = 1/tanθ = 1/ 1/√3 = √3

cscθ = 1/sinθ = 1/ 1/2 = 2

secθ = 1/cosθ = 1/ √3/2 =2/√3.

Therefore, the other five ratios are

cosθ = √3/2, tanθ = 1/√3, cotθ = √3, cscθ = 2, secθ = 2/√3.

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If sin θ = 1/2 and angle θ is acute, how do you find the other five ratios?

Summary:

If sin θ = 1/2 and angle θ is acute, the other five ratios are cosθ = √3/2, tanθ = 1/√3, cotθ = √3, cscθ = 2, secθ = 2/√3.