Given the expression:
sin(135° - 60°)
Let's find the exact value of the expression.
First simplify the expression in the parentheses:
sin(135° - 60°) = sin(75°)
The exact value of sin(75°) is:
[tex]sin(75^o)=\frac{\sqrt{2}+\sqrt{6}}{4}[/tex]
Part B.
Given the expression:
sin135° - cos60°
Let's find the exact value.
Apply the reference by finding the equivalent angle in the first quadrant.
[tex]\begin{gathered} 135-90=45^o \\ \\ \text{ Thus, we have:} \\ sin45-cos60 \end{gathered}[/tex]
We have the following:
[tex]\begin{gathered} Exact\text{ value of sin45=}\frac{\sqrt{2}}{2} \\ \\ Exact\text{ value of cos60=}\frac{1}{2} \end{gathered}[/tex]
Therefore, the exact value of the expression is:
[tex]\frac{\sqrt{2}}{2}=\frac{1}{2}[/tex]
ANSWER:
• Part A.
[tex]\begin{gathered} \frac{\sqrt{2}+\sqrt{6}}{4} \\ \end{gathered}[/tex]
• Part B.
[tex]\frac{\sqrt{2}}{2}-\frac{1}{2}[/tex]
