Question

Find sin 75° using trigonometric ratios of
45°
and
30​°​

Answer 1

Answer:

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Precalculus

 

Find the Exact Value sin(75)

sin(75)sin(75)

Split 7575 into two angles where the values of the six trigonometric functions are known.

sin(30+45)sin(30+45)

Apply the sum of angles identity.

sin(30)cos(45)+cos(30)sin(45)sin(30)cos(45)+cos(30)sin(45)

The exact value of sin(30)sin(30) is 1212.

12cos(45)+cos(30)sin(45)12cos(45)+cos(30)sin(45)

The exact value of cos(45)cos(45) is √2222.

12⋅√22+cos(30)sin(45)12⋅22+cos(30)sin(45)

The exact value of cos(30)cos(30) is √3232.

12⋅√22+√32sin(45)12⋅22+32sin(45)

The exact value of sin(45)sin(45) is √2222.

12⋅√22+√32⋅√2212⋅22+32⋅22

Simplify 12⋅√22+√32⋅√2212⋅22+32⋅22.

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√2+√642+64

The result can be shown in multiple forms.

Exact Form:

√2+√642+64

Decimal Form: