Q: Which of the following is the correct reciprocal identity for $$\tan \theta$$?

$$\tan \theta = \dfrac{1}{\cot \theta}$$

Q: Which trigonometric functions are positive in Quadrant III?

$$\tan \theta$$ and $$\cot \theta$$

Q: Determine if $$\sin \theta = 2.5 is $$possible for any real $$\theta.$$

Impossible, because $$-1 \leq \sin \theta \leq 1$$

Q: Given $$\tan \theta = 110.47$$, is this value possible for some $$\theta$$?

Yes, because $$\tan \theta$$ can take any real value

Q: If $$\sec \theta = 0.6$$, is this value possible for any real $$\theta$$?

No, because $$|\sec \theta| \geq 1$$

Q: Which of the following is a Pythagorean identity?

$$\sin^2$ \theta + \cos^2$ \theta = 1$$

Q: Which quotient identity correctly expresses $$\tan \theta in $$terms of $$\sin \theta$$ and $$\cos \theta$$?

$$\tan \theta = \dfrac{\sin \theta}{\cos \theta}$$

Q: A surveyor measures an angle of $$300^\circ$$ from the positive $$x-$$axis. Which trigonometric functions are positive for this angle?

$$\cos \theta$$ and $$\sec \theta$$

Q: Which of the following statements about the range of $$\tan \theta is $$correct?

$$\tan \theta$$ can take any real value

Q: Given $$\cos \theta = a$$ and $$a \u003e 0$$, what is $$\sin \theta$$ using the Pythagorean identity?

$$\sin \theta = \sqrt{1 - a^2$}$$

Question 1

Which of the following is the correct reciprocal identity for $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \dfrac{1}{\cot 	heta}$$

Question 2

Given $$\sec 	heta = \dfrac{5}{3}$$, what is $$\cos 	heta$$?

Accepted Answer

$$\dfrac{3}{5}$$

Question 3

If $$\csc 	heta = -\dfrac{\sqrt{12}}{2}$$, what is $$\sin 	heta$$?

Accepted Answer

$$-\dfrac{\sqrt{3}}{3}$$

Question 4

In which quadrant is $$\sin 	heta \u003e 0$$ and $$	an 	heta \u003c 0$$?

Accepted Answer

Quadrant II

Question 5

Which trigonometric functions are positive in Quadrant III?

Accepted Answer

$$	an 	heta$$ and $$\cot 	heta$$

Question 6

Determine if $$\sin 	heta = 2.5 is $$possible for any real $$	heta.$$

Accepted Answer

Impossible, because $$-1 \leq \sin 	heta \leq 1$$

Question 7

Given $$	an 	heta = 110.47$$, is this value possible for some $$	heta$$?

Accepted Answer

Yes, because $$	an 	heta$$ can take any real value

Question 8

If $$\sec 	heta = 0.6$$, is this value possible for any real $$	heta$$?

Accepted Answer

No, because $$|\sec 	heta| \geq 1$$

Question 9

Suppose $$\sin 	heta = \dfrac{2}{3}$$ and $$	heta is in $$Quadrant II. What is $$\cos 	heta$$?

Accepted Answer

$$-\dfrac{\sqrt{5}}{3}$$

Question 10

Given $$	an 	heta = -2$$ and $$	heta is in $$Quadrant III, what is the sign of $$\sin 	heta$$ and $$\cos 	heta$$?

Accepted Answer

Both are negative

Question 11

Which of the following is a Pythagorean identity?

Accepted Answer

$$\sin^2$ 	heta + \cos^2$ 	heta = 1$$

Question 12

If $$\cos 	heta = -\dfrac{2}{5}$$ and $$	heta is in $$Quadrant III, what is $$\sin 	heta$$?

Accepted Answer

$$-\dfrac{\sqrt{21}}{5}$$

Question 13

Which quotient identity correctly expresses $$	an 	heta in $$terms of $$\sin 	heta$$ and $$\cos 	heta$$?

Accepted Answer

$$	an 	heta = \dfrac{\sin 	heta}{\cos 	heta}$$

Question 14

A surveyor measures an angle of $$300^\circ$$ from the positive $$x-$$axis. Which trigonometric functions are positive for this angle?

Accepted Answer

$$\cos 	heta$$ and $$\sec 	heta$$

Question 15

If $$\sin 	heta = \dfrac{4}{5}$$ and $$	heta is in $$Quadrant II, what is $$	an 	heta$$?

Accepted Answer

$$-\dfrac{4}{3}$$

Question 16

Which of the following statements about the range of $$	an 	heta is $$correct?

Accepted Answer

$$	an 	heta$$ can take any real value

Question 17

Given $$\cos 	heta = a$$ and $$a \u003e 0$$, what is $$\sin 	heta$$ using the Pythagorean identity?

Accepted Answer

$$\sin 	heta = \sqrt{1 - a^2$}$$

Question 18

A pilot is flying in Quadrant IV. Which trigonometric functions are positive for the angle of elevation?

Accepted Answer

$$\cos 	heta$$ and $$\sec 	heta$$

Question 19

If $$\cot 	heta = 0$$, what is $$	an 	heta$$?

Accepted Answer

$$	an 	heta is $$undefined

Trigonometric Functions: Definitions, Identities, and Signs

Guida di studio - Domande di pratica

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