Answer:
The values of the trigonometric functions of t
[tex]$\sin t=-\frac{\sqrt{3} }{2}[/tex]
[tex]\cos t=\frac{1}{2},[/tex]
[tex]\tan t=-\sqrt{3}[/tex]
[tex]$\csc t-\frac{2}{\sqrt{3} }[/tex]
[tex]\sec t=2[/tex]
[tex]\cot t=\frac{1}{\sqrt{3} }[/tex]
Step-by-step explanation:
Given:
[tex]\sec(t)=2[/tex]
The terminal point of [tex]t[/tex] is in Quadrant [tex]IV[/tex]
Step 1:
To find the values of trigonometric functions of t
[tex]\sec(t)=\frac{H}{A}[/tex]
[tex]=\frac{2}{1}[/tex]
Analyze the figure and find the value of O
[tex]t[/tex] ∈ [tex]IV[/tex]
[tex]O=\sqrt{2^{2}-1^{2} }[/tex]
[tex]=\sqrt{4-1}[/tex]
[tex]=\sqrt{3}[/tex]
Step 2:
[tex]$\sin t=-\frac{O}{H}[/tex]
[tex]=-\frac{\sqrt{3} }{2}[/tex]
[tex]\cos t=\frac{A}{H}[/tex]
[tex]=\frac{1}{2}[/tex]
[tex]\tan t=-\frac{O}{A}[/tex]
[tex]=-\sqrt{3}[/tex]
[tex]$\csc t=-\frac{H}{O}[/tex]
[tex]=-\frac{2}{\sqrt{3} }[/tex]
[tex]\sec t=\frac{H}{A}[/tex]
[tex]=\frac{2}{1}[/tex]
[tex]\cot t=-\frac{A}{O}[/tex]
[tex]=\frac{1}{\sqrt{3} }[/tex]
Learn more about trigonometry functions, refer:
