Q: If the terminal side of an angle $$\theta in $$standard position passes through the point $$(8, 15)$$, what is $$\sin \theta$$?

$$\sin \theta = \frac{15}{17}$$

Question 1

Given a point $$P(x, y) on $$the terminal side of an angle $$	heta in $$standard position, what is the formula for the distance $$r$$ from the origin to $$P$$?

Accepted Answer

$$r = \sqrt{x^2$ + y^2$}$$

Question 2

If the terminal side of an angle $$	heta in $$standard position passes through the point $$(8, 15)$$, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = \frac{15}{17}$$

Question 3

Which trigonometric functions are undefined for a quadrantal angle whose terminal side lies along the y-axis?

Accepted Answer

Tangent and secant

Question 4

A surveyor stands at $$(0,0)$$ and sights a point at $$(3,4). $$What is the value of $$	an 	heta$$ for the angle $$	heta$$ formed?

Accepted Answer

$$	an 	heta = \frac{4}{3}$$

Question 5

If the point $$(-3, -4) is on $$the terminal side of an angle $$	heta$$, what is $$\sec 	heta$$?

Accepted Answer

$$\sec 	heta = \frac{5}{-3}$$

Question 6

A ladder leans against a wall, forming an angle $$	heta$$ with the ground. If the base is $$8 ft $$from the wall and the top is $$15 ft $$above the ground, what is the length of the ladder?

Accepted Answer

$$\sqrt{8^2$ + 15^2$} = 17 ft$$

Question 7

Which of the following is the correct definition of $$\cot 	heta in $$terms of $$x$$ and $$y$$?

Accepted Answer

$$\cot 	heta = \frac{x}{y}$$

Question 8

A point $$(2, -1)$$ lies on the terminal side of an angle $$	heta. $$What is $$r$$?

Accepted Answer

$$r = \sqrt{2^2$ + (-1)^2$} = \sqrt{5}$$

Question 9

If $$x = 0$$ and $$y = 1$$, what is $$\cos 90^\circ$$?

Accepted Answer

$$\cos 90^\circ = 0$$

Question 10

A student calculates $$\sin 30^\circ on $$their calculator and gets $$-0.988. $$What is the most likely error?

Accepted Answer

Calculator is set to radian mode

Question 11

If the terminal side of an angle $$	heta$$ passes through $$(0, -3)$$, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = -1$$

Question 12

Which trigonometric function is undefined for the angle whose terminal side passes through $$(3, 0)$$?

Accepted Answer

Cotangent

Question 13

Given $$x = -3$$, $$y = -4$$, and $$r = 5$$, what is $$\cos 	heta$$?

Accepted Answer

$$\cos 	heta = \frac{-3}{5}$$

Question 14

A pilot flies from $$(0,0) to$$ $$(8,15). $$What is the value of $$\sec 	heta$$ for the angle $$	heta$$ formed?

Accepted Answer

$$\sec 	heta = \frac{17}{8}$$

Question 15

If $$x = 2$$ and $$y = -1$$, what is $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \frac{-1}{2}$$

Question 16

A construction worker needs to find the angle $$	heta$$ such that $$\sin 	heta = \frac{4}{5}$$ and $$\cos 	heta = \frac{3}{5}. $$What is $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \frac{4}{3}$$

Question 17

If $$x = 0$$ and $$y = 1$$, what is $$	an 90^\circ$$?

Accepted Answer

$$	an 90^\circ is $$undefined

Question 18

Which of the following is the correct definition of $$\sec 	heta in $$terms of $$r$$ and $$x$$?

Accepted Answer

$$\sec 	heta = \frac{r}{x}$$

Question 19

A point $$(0, -3) is on $$the terminal side of an angle $$	heta. $$What is $$\cot 	heta$$?

Accepted Answer

$$\cot 	heta is $$undefined

Trigonometric Functions: Definitions, Applications, and Quadrantal Angles

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