Question

Find the value of sin75°

Answer 1

I Hope it will help u

Answer 2

Value of $\bf \red{sin {75}^{ \circ} = \frac{ \sqrt{3} + 1}{2 \sqrt{2} } }$ or $\bf \red{sin {75}^{ \circ} = 0.966}$

Given:

• $sin \: {75}^{ \circ}$

To find:

• Find the value of trigonometric angle.

Solution:

Formula to be used:

$\bf \sin(A+B) = \sin(A) \cos(B) + \cos(A) \sin(B)$

Step 1:

Rewrite the expression so that above written formula can be used.

$sin \: {75}^{ \circ} =sin( {45}^{ \circ} + {30}^{ \circ})$

Now open RHS as per formula.

$sin( {45}^{ \circ} + {30}^{ \circ}) =sin \: {45}^{ \circ} cos {30}^{ \circ} +cos \: {45}^{ \circ} sin {30}^{ \circ}$

Step 2:

Put the values of all angles.

We know that

$sin \: {45}^{ \circ} = cos {45}^{ \circ} = \frac{1}{ \sqrt{2} }$

$sin \: {30}^{ \circ} = \frac{1}{2}$

and

$cos {30}^{ \circ} = \frac{ \sqrt{3} }{2}$

So,

$sin {75}^{ \circ} = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{2}$

or

$sin {75}^{ \circ} = \frac{ \sqrt{3} }{2 \sqrt{2} } + \frac{1}{ 2\sqrt{2} }$

or

$\bf sin {75}^{ \circ} = \frac{ \sqrt{3} + 1}{2 \sqrt{2} }$

or

put values of √2=1.414 and √3= 1.732

$sin {75}^{ \circ} = \frac{1.732 + 1}{2 \times 1.414}$

or

$sin {75}^{ \circ} = \frac{2.732}{2.828}$

or

$\bf sin {75}^{ \circ} = 0.966$

Thus,

Value of $\bf sin {75}^{ \circ} = \frac{ \sqrt{3} + 1}{2 \sqrt{2} }$ or $\bf sin {75}^{ \circ} = 0.966$

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