Find the value of x.

Mathematics

1 answer:

koban [17]3 years ago

8 0

Answer:

x = 110°

Step-by-step explanation:

The Outside Angle Theorem states that the measure of the angle formed by two secants or a secant and tangent from a point outside of a circle is half the difference between the two arcs.

This means that ½ (210 – x) = 50.

½ ( 210 – x ) × 2 = 50 × 2

210 – x = 100.

210 – x + x = 100 + x.

210 = 100 + x.

100 + x = 210.

100 + x – 100 = 210 – 100.

x = 110.

This value must be true because:

½ ( 210 – 110 ) = 50.

½ ( 100 ) = 50.

50 = 50.

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

mariarad [96]

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

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