Q: Given $$P(-8, 15) is on $$the terminal side of angle $$\theta$$, what is $$\sin \theta$$?

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

Q: A ladder leans against a wall, forming an angle $$\theta$$ with the ground. If the top of the ladder is $$12$$ feet above the ground and the base is $$5$$ feet from the wall, what is $$\tan \theta$$?

$$\tan \theta = \dfrac{12}{5}$$

Q: Which of the following is the correct definition of $$\sec \theta in $$terms of $$x$$, $$y$$, and $$r$$?

$$\sec \theta = \dfrac{r}{x}$$, \quad x \neq 0$

Q: A surveyor stands at point $$A(0, 0)$$ and measures the angle of elevation to the top of a building at point $$B(0, 10). $$What is $$\sin \theta if $$the surveyor is $$10$$ units away from the building along the $$x-$$axis?

$$\sin \theta = \dfrac{10}{\sqrt{200}}$$

Q: If $$\theta is an $$angle in standard position and $$P(-3, 4) is on $$its terminal side, what is $$\tan \theta$$?

$$\tan \theta = \dfrac{4}{-3}$$

Q: A person stands $$15$$ meters from a building and looks up to the top, which is $$20$$ meters high. What is $$\sin \theta$$, where $$\theta is $$the angle of elevation?

$$\sin \theta = \dfrac{20}{25}$$

Question 1

Given a right triangle with legs of lengths $$a = 5$$ and $$b = 12$$, what is the length of the hypotenuse $$c$$?

Accepted Answer

$$c = 13$$

Question 2

If $$P(3, 4) is a $$point on the terminal side of angle $$	heta in $$standard position, what is $$r$$, the distance from the origin to $$P$$?

Accepted Answer

$$r = 5$$

Question 3

Given $$P(-8, 15) is on $$the terminal side of angle $$	heta$$, what is $$\sin 	heta$$?

Accepted Answer

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

Question 4

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

Accepted Answer

Tangent and secant

Question 5

A ladder leans against a wall, forming an angle $$	heta$$ with the ground. If the top of the ladder is $$12$$ feet above the ground and the base is $$5$$ feet from the wall, what is $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \dfrac{12}{5}$$

Question 6

If $$	heta is a $$quadrantal angle with terminal side on the negative $$x-$$axis, what is $$\cos 	heta$$?

Accepted Answer

$$\cos 	heta = -1$$

Question 7

Given $$P(0, -1) is on $$the terminal side of angle $$	heta$$, which trigonometric functions are undefined?

Accepted Answer

Tangent and secant

Question 8

A ship sails from point $$A(2, 3) to $$point $$B(8, 15). $$What is the distance traveled by the ship?

Accepted Answer

$$\sqrt{180}$$

Question 9

If $$\sin 	heta = \dfrac{3}{5}$$ and $$	heta is in $$standard position with $$r \u003e 0$$, which of the following could be the coordinates of a point on the terminal side of $$	heta$$?

Accepted Answer

$$(4, 3)$$

Question 10

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

Accepted Answer

$$\sec 	heta = \dfrac{r}{x}$$, \quad x 
eq 0$

Question 11

A surveyor stands at point $$A(0, 0)$$ and measures the angle of elevation to the top of a building at point $$B(0, 10). $$What is $$\sin 	heta if $$the surveyor is $$10$$ units away from the building along the $$x-$$axis?

Accepted Answer

$$\sin 	heta = \dfrac{10}{\sqrt{200}}$$

Question 12

If $$	heta is an $$angle in standard position and $$P(-3, 4) is on $$its terminal side, what is $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \dfrac{4}{-3}$$

Question 13

Which trigonometric function is always positive for any point $$(x, y) in $$the first quadrant?

Accepted Answer

Sine, cosine, and tangent

Question 14

A drone flies from $$(1, 2) to$$ $$(4, 6). $$What is the distance it travels?

Accepted Answer

$$5$$

Question 15

If $$	heta is a $$quadrantal angle with terminal side on the positive $$x-$$axis, what is $$\csc 	heta$$?

Accepted Answer

$$\csc 	heta is $$undefined

Question 16

If $$\cos 	heta = 0$$ and $$	heta is a $$quadrantal angle, what is the possible value of $$	heta in $$degrees?

Accepted Answer

$$90^\circ or$$ $$270^\circ$$

Question 17

A ramp rises $$6$$ feet over a horizontal distance of $$8$$ feet. What is the length of the ramp?

Accepted Answer

$$10$$ feet

Question 18

If $$\cot 	heta = \dfrac{x}{y}$$, which of the following must be true?

Accepted Answer

$$y 
eq 0$$

Question 19

A person stands $$15$$ meters from a building and looks up to the top, which is $$20$$ meters high. What is $$\sin 	heta$$, where $$	heta is $$the angle of elevation?

Accepted Answer

$$\sin 	heta = \dfrac{20}{25}$$

Trigonometric Functions: Definitions, Properties, and Quadrantal Angles

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