Answer: [tex]\frac{4\sqrt{3} }{3} +\frac{1}{2}[/tex]
Step-by-step explanation:
You can either do this manually or use your calculator. Using your calculator, make sure that your calculator is in degree mode, then enter tan(30) + (1/tan(30)) + sin(60). [1/tan(30) is equal to cot(30) because tangent and cotangent are inverse functions].
Manually, use the unit circle. Tangent is sine over cosine. Sine of 30 degrees is 1/2. Cosine of 30 degrees is [tex]\sqrt{3} /2[/tex]. 1/2 divided by [tex]\sqrt{3}/2[/tex] is [tex]\sqrt{3}/3[/tex]. Cotangent is 1/tangent so take 1/[tex]\sqrt{3}/3[/tex] which is [tex]\sqrt{3}[/tex]. Then we already said that sine of 30 degrees is 1/2, so add them all together.
[tex]\sqrt{3}/3+\sqrt{3}+\frac{1}{2}[/tex] which is equal to [tex]\frac{4\sqrt{3} }{3} +\frac{1}{2}[/tex] or approximately 2.8094.
