To determine whether the given trigonometric statements are true or false, let's first recall the exact values of the trigonometric functions for a 30-degree angle.
1. Sine of 30 degrees:
[tex]\[\sin 30^{\circ} = \frac{1}{2}\][/tex]
2. Cosine of 30 degrees:
[tex]\[\cos 30^{\circ} = \frac{\sqrt{3}}{2}\][/tex]
Given the statements:
- [tex]\(\sin 30^{\circ}=\frac{\sqrt{3}}{2}\)[/tex]
- [tex]\(\cos 30^{\circ}=\frac{1}{2}\)[/tex]
Now compare these given statements with the known exact values:
- The statement [tex]\(\sin 30^{\circ}=\frac{\sqrt{3}}{2}\)[/tex] is incorrect because [tex]\(\sin 30^{\circ} = \frac{1}{2}\)[/tex], not [tex]\(\frac{\sqrt{3}}{2}\)[/tex].
- The statement [tex]\(\cos 30^{\circ}=\frac{1}{2}\)[/tex] is incorrect because [tex]\(\cos 30^{\circ} = \frac{\sqrt{3}}{2}\)[/tex], not [tex]\(\frac{1}{2}\)[/tex].
Therefore, since both statements do not match the known exact values of [tex]\(\sin 30^{\circ}\)[/tex] and [tex]\(\cos 30^{\circ}\)[/tex], the correct answer is:
B. False
