Question

the value of sin 106° is??​

Answer 1

Answer:

Step-by-step explanation:

Sin 106°

Lies in 2nd Quad so +be sign

+Sin(90+16). Here sin changes to cos since there is 90

Cos(16°)

Cos(53-37)

Cos(A-B)=CosACosB+SinASinB

=Cos53°Cos37+Sin53°Sin37°

=(3/5)*(4/5)+(4/5)*(3/5)

=12/25+12+25

=24/25

Thank you

Hope it is correct

Answer 2

Given:

• Sin 106°

To Find:

• The value of Sin 106°

Solution:

Sin 106° lies in the second quadrant.

We can write Sin 106° as Sin(90+16)°.

In the next step, Sin will change into cos as there is 90°.

∴  Sin(90+16)° = cos(16°)

⇒ Sin(90+16)° = cos(53-37)

The above equation is in the form ,

cos(A-B) = cos(A)×cos(B)+sin(A)×sin(B), where "A = 53° and B = 37°".

⇒ cos(53°-37°) = cos(53°)×cos(37°)+sin(53°)×sin(37°)

⇒ cos(53°-37°) = (3/5×4/5)+(4/5×3/5) {the denominators are same so we can directly multiply the fractions}

⇒ cos(53°-37°)  = 12/5+12/5 = 24/25 {adding the fractions directly as the denominators are same}

⇒  Sin 106° = 24/25

∴ The value of Sin 106° = 24/25