Question

Find the values of the trigonometric functions of ∅ from the information given.tan(∅) = -2, sin(∅) > 0

Answer 1

`\tan \emptyset=-2,\sin \emptyset>0`

Call tan ∅ = t = -2, Use the trig identity:

`\cos ^2\emptyset=(1)/(1+t^2)`

Since tan ∅ = -3 is negative and sin ∅ > 0, then ∅ should be in quadrant II

`\begin{gathered} \cos ^2\emptyset=(1)/(1+4)=(1)/(5)=0.2 \\ \cos ^2\emptyset=0.2 \\ \cos \emptyset=-0.45 \end{gathered}`
`\begin{gathered} \sin ^2\emptyset=1-\cos ^2\emptyset=1-0.2=0.8 \\ \sin ^2\emptyset=0.8 \\ \sin \emptyset=0.89,\text{ }\mleft(QuadrantII\mright) \end{gathered}`
`\cot \emptyset=-(1)/(2)`
`co\sec \emptyset=(1)/(\sin\emptyset)=(1)/(0.894)=1.12`
`\sec \emptyset=(1)/(\cos\emptyset)=(1)/(-0.447)=-2.24`