Step-by-step explanation:
tan is opposite over adjacent which gives you the side lengths. Use Pythagorean Theorem to find the hypotenuse. 1² + 3² = c² ⇒ √10 = c
opposite = 1, adjacent = 3, hypotenuse = √10
Answers:
sin = [tex]\frac{opposite}{hypotenuse} = \frac{1}{\sqrt{10}} *\frac{\sqrt{10} }{\sqrt{10} } =\frac{\sqrt{10} }{10}[/tex]
cos = [tex]\frac{adjacent}{hypotenuse} = \frac{3}{\sqrt{10}} *\frac{\sqrt{10} }{\sqrt{10} } =\frac{3\sqrt{10} }{10}[/tex]
csc = [tex]\frac{hypotenuse}{opposite} = \frac{\sqrt{10}}{1} =\sqrt{10}[/tex]
sec = [tex]\frac{hypotenuse}{adjacent} = \frac{\sqrt{10}}{3}[/tex]
cot = [tex]\frac{adjacent}{opposite} = \frac{3}{1} = 3[/tex]
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Step-by-step explanation:
The graph provides the adjacent side and hypotenuse. Use Pythagorean Theorem to find the opposite side. (√15)² + b² = (2√5)² ⇒ b = √5
opposite = √5, adjacent = √15, hypotenuse = 2√5
Answers:
sin = [tex]\frac{opposite}{hypotenuse} = \frac{\sqrt{5}}{2\sqrt{5}} =\frac{1}{2}[/tex]
cos = [tex]\frac{adjacent}{hypotenuse} = \frac{\sqrt{15}}{2\sqrt{5}} =\frac{\sqrt{3} }{2}[/tex]
tan = [tex]\frac{opposite}{adjacent} = \frac{\sqrt{5}}{\sqrt{15}}= \frac{1}{\sqrt{3}} *\frac{\sqrt{3} }{\sqrt{3}} =\frac{\sqrt{3} }{3}[/tex]
csc = [tex]\frac{hypotenuse}{opposite} = \frac{2\sqrt{5}}{\sqrt{5}} =2[/tex]
sec = [tex]\frac{hypotenuse}{adjacent} = \frac{2\sqrt{5}}{\sqrt{15}}= \frac{2}{\sqrt{3}}*\frac{\sqrt{3} }{\sqrt{3}}=\frac{2\sqrt{3}}{3}[/tex]
cot = [tex]\frac{adjacent}{opposite} = \frac{\sqrt{15}}{\sqrt{5}} = \sqrt{3}[/tex]
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sec [tex]\frac{4\pi} {11}[/tex]
= cos [tex]\frac{11}{4\pi}[/tex]
= cos 1.14
= 0.9998
