Respuesta :
Answer:
Step-by-step explanation:
sin(θ) = 2/7
sin²(θ) +cos²(θ) =1
[tex](\frac{2}{7})^{2} +cos^2(theta)=1 \\\\cos^2(theta)=1-(\frac{4}{49} )=\frac{49}{49}-\frac{4}{49} =\frac{45}{49} \\ \\cos(theta)=+/-\sqrt{\frac{45}{49} } =+/-\frac{3\sqrt{5} }{7}[/tex]
[tex]Answer \\ is \frac{3\sqrt{5} }{7}[/tex]
Answer is positive because tangent is positive, sin is also positive, and tan=sin/cos.
The values of sin θ and tan θ from the given value of cos θ are; sin θ = 2/7 and cos θ = (3√5 )/7.
How to write Trigonometric ratios?
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}[/tex]
We have been given that
sin θ = 2/7
Now, from trigonometric ratios, we know that;
cos θ = adj/hyp
sin θ = opp/hyp
tan θ = sin θ/cos θ
From right-angled triangle;
adj = √(7² - 2²)
adj = √45
adj = 3√5
Thus;
cos θ = (3√5 )/7
tan θ = (2/7) / ((3√5)/7)
tan θ = 2/ (3√5 )
The values of sin θ and tan θ from the given value of cos θ are; sin θ = 2/7 and cos θ = (3√5 )/7.
Read more about Trigonometric Ratios at; brainly.com/question/11967894
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