Question

I have a trigonometric question I will upload a photo

Answer 1

The secant can be calculated as the inverse of the cosine, so we have:

`\sec (-(7\pi)/(3))=(1)/(\cos (-(7\pi)/(3)))=(1)/(0.5)=2`

The cosecant can be calculated as the inverse of the sine, so we have:

`\csc (-(7\pi)/(3))=(1)/(\sin(-(7\pi)/(3)))=\frac{1}{\frac{\sqrt[]{3}}{2}}=\frac{2}{\sqrt[]{3}}=\frac{2\sqrt[]{3}}{3}=1.1547`

The tangent can be calculated as the sine over the cosine, so we have:

`\tan (-(7\pi)/(3))=(\sin(-(7\pi)/(3)))/(\cos(-(7\pi)/(3)))=\frac{\frac{\sqrt[]{3}}{2}}{0.5}=\sqrt[]{3}=1.732`

The cotangent can be calculated as the inverse of the tangent, so we have:

`\cot (-(7\pi)/(3))=(1)/(\tan(-(7\pi)/(3)))=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{3}=0.57735`