Question

What is the value of trigonometry ratio sin 165????​

Answer 1

Answer:

Explanation:

Some things we will use:

sin

(

θ

)

=

sin

(

180

∘

−

θ

)

sin

(

α

−

β

)

=

sin

α

cos

β

−

sin

β

cos

α

sin

45

∘

=

cos

45

∘

=

√

2

2

sin

30

∘

=

1

2

cos

30

∘

=

√

3

2

Hence we find:

sin

165

∘

=

sin

(

180

∘

−

165

∘

)

sin

165

∘

=

sin

15

∘

sin

165

∘

=

sin

(

45

∘

−

30

∘

)

sin

165

∘

=

sin

45

∘

cos

30

∘

−

sin

30

∘

cos

45

∘

sin

165

∘

=

√

2

2

√

3

2

−

1

2

√

2

2

sin

165

∘

=

1

4

(

√

6

−

√

2

)

Footnotes

The trigonometric values we used in our derivation can be observed in the following right angled triangles:

enter image source here

Hence

sin

45

∘

=

cos

45

∘

=

1

√

2

=

√

2

2

enter image source here

Hence

sin

30

∘

=

1

2

and

cos

30

∘

=

√

3

2

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