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ivolga24 [154]
3 years ago
11

Angle (theta) is in standard position. If (8,-15) is on the terminal ray of angle (theta), find the values of the trigonometric

functions.
sin(theta)=
cos(theta)=
tan(theta)=
csc(theta)=
sec(theta)=
col(theta)=

What are the answers and how?

Mathematics
1 answer:
mariarad [96]3 years ago
6 0

Answer:

\sin \theta =\frac{-15}{17}\\cos \theta =\frac{8}{17}\\\tan  \theta =\frac{-15}{8}\\\csc \theta =\frac{-17}{15}\\\sec \theta =\frac{17}{8}\\\cot \theta =\frac{-8}{15}

Step-by-step explanation:

Given: (8,-15) is on the terminal ray of angle

To find: All the trigonometric ratios

Solution:

Trigonometry is a  branch of mathematics that explain relationship between the sides and angles of triangles.

If (x, y) lies on the terminal side of  θ  then r=\sqrt{x^2+y^2}

r=\sqrt{(8)^2+(-15)^2}=\sqrt{64+225}=\sqrt{289}=17 units

\sin \theta =\frac{y}{r}=\frac{-15}{17}\\cos \theta =\frac{x}{r}=\frac{8}{17}\\\tan  \theta =\frac{y}{x}=\frac{-15}{8}\\\csc \theta =\frac{1}{\sin \theta }=\frac{-17}{15}\\\sec \theta =\frac{1}{cos \theta}=\frac{17}{8}\\\cot \theta =\frac{1}{\tan  \theta}=\frac{-8}{15}

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