Mathematics: Find an exact value. sin 15°

Find an exact value. sin 15° - id154374383, byers024

Lucialari4345

17.06.2020

$sin(15^o)= (\frac{\sqrt{6}-\sqrt{2}}{4})$

Step-by-step explanation:

we know that

sin(A-B)= sin(A)cos(B)-cos(A)sin(B)

Let

A=60^o

B=45^o

A-B=60^o-45^o=15^o

substitute

sin(60^o-45^o)= sin(60^o)cos(45^o)-cos(60^o)sin(45^o)

sin(15^o)= sin(60^o)cos(45^o)-cos(60^o)sin(45^o)

Remember that

$sin(60^o)=\frac{\sqrt{3}}{2}$

$cos(60^o)=\frac{1}{2}$

$sin(45^o)=\frac{\sqrt{2}}{2}$

$cos(45^o)=\frac{\sqrt{2}}{2}$

substitute

$sin(15^o)= (\frac{\sqrt{3}}{2})(\frac{\sqrt{2}}{2})-(\frac{1}{2})(\frac{\sqrt{2}}{2})$

$sin(15^o)= (\frac{\sqrt{6}}{4})-(\frac{\sqrt{2}}{4})$

Simplify

$sin(15^o)= (\frac{\sqrt{6}-\sqrt{2}}{4})$

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Parmenter

01.12.2022

The solutions to the equation are 1, 0.375.

Step-by-step explanation:

The equation is already in factored form.

The solutions to the system are the values of x that make one or the other of the factors be zero.

x -1 = 0 . . . when x = 1

8x -3 = 0 . . . when x = 3/8 = 0.375

There is only one variable, so no "ordered pairs" are involved.

The solutions are {1, 0.375}.

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