Respuesta :
Answer:
STEP 3
Step-by-step explanation:
Francesca drew point (–2, –10) on the terminal ray of angle [tex]\Theta[/tex], which is in standard position. She found values for the six trigonometric functions using the steps below.
Step 1
A unit circle is shown. A ray intersects point (negative 2, negative 10) in quadrant 3. Theta is the angle formed by the ray and the x-axis in quadrant 1.
Step 2
[tex]r = (\sqrt{(-2)^2+(-10)^2}=\sqrt{104}=2\sqrt{26[/tex]
Step 3
[tex]Sin \theta = \frac{-2}{2\sqrt{26} }=-\frac{1}{\sqrt{26} }=-\frac{\sqrt{26}}{26 }[/tex]
[tex]cos \theta = \frac{-10}{2\sqrt{26} }=-\frac{5}{\sqrt{26} }=-\frac{5\sqrt{26}}{26 }[/tex]
[tex]tan \theta = \frac{2}{-10 }=-\frac{1}{5}\\[/tex]
[tex]cosec \theta = \frac{1}{sin \theta}=\frac{1}{-\frac{\sqrt{26}}{26 }}=-\frac{\sqrt{26}}{5}[/tex]
[tex]Secant \theta = 1/cos \theta =\frac{1}{-\frac{5\sqrt{26} }{26} } =-\frac{\sqrt{26}}{5} \\cotangent \theta=1/tan \theta=\frac{1}{1/5} =5[/tex]
Francesca made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also resulted in incorrect cosecant, secant, and tangent functions.
The correct values are:
[tex]Sin \theta = \frac{-10}{2\sqrt{26} }=-\frac{5}{\sqrt{26} }=-\frac{5\sqrt{26} }{26}\\cos \theta = \frac{-2}{2\sqrt{26} }=-\frac{1}{\sqrt{26} }=-\frac{\sqrt{26} }{26}\\tan \theta = \frac{-10}{-2}=5[/tex]
Answer:
D.She made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also results in incorrect cosecant, secant, and tangent functions.
Step-by-step explanation:
on e 2020