Lecture 21 Nov 14 SEAN

Front

What is the exact value of \( \tan^2(75\degree) \)?

Back

The exact value is \( 7 + 4\sqrt{3} \).

Front

What is the exact value of \( \sin(15\degree) \cdot \cos(15\degree) \)?

Back

The exact value is \( \frac{\sqrt{3}}{4} \).

Front

What is the half-angle formula for sine?

Back

The half-angle formula for sine is \( \sin\left(\frac{\theta}{2}\right) = \sqrt{\frac{1 - \cos(\theta)}{2}} \).

Front

How do you find \( \sin(105\degree) \) using the half-angle formula?

Back

Use the half-angle formula: \( \sin(105\degree) = \sin(90\degree + 15\degree) = \sin(90\degree)\cos(15\degree) + \cos(90\degree)\sin(15\degree) \).

Front

What is the value of \( \sin(15\degree) \)?

Back

The value of \( \sin(15\degree) \) is \( \frac{\sqrt{6} - \sqrt{2}}{4} \).

Front

What is the value of \( \cos(15\degree) \)?

Back

The value of \( \cos(15\degree) \) is \( \frac{\sqrt{6} + \sqrt{2}}{4} \).

Front

What is the relationship between tangent and sine/cosine?

Back

The relationship is given by \( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \).

Front

What is the exact value of \( \tan(75\degree) \)?

Back

The exact value is \( 2 + \sqrt{3} \).

Front

What is the sine of a sum formula?

Back

The sine of a sum formula is \( \sin(a + b) = \sin(a)\cos(b) + \cos(a)\sin(b) \).

Front

What is the cosine of a sum formula?

Back

The cosine of a sum formula is \( \cos(a + b) = \cos(a)\cos(b) - \sin(a)\sin(b) \).