Q: Which of the following is a Pythagorean identity?

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

Q: Which reciprocal identity is correct?

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

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

No, because $$\sec \theta$$ must be $$\leq -1 or$$ $$\geq 1$$

Q: Which of the following is a quotient identity?

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

Q: If $$\sin \theta = \frac{y}{r}$$ and $$\cos \theta = \frac{x}{r}$$, which identity is always true?

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

Question 1

Given a point $$P(-3, 4) on $$the terminal side of an angle $$	heta in $$standard position, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{4}{5}$$

Question 2

Which of the following is the correct definition of $$\sec 	heta$$ for a point $$(x, y) on $$the terminal side of $$	heta$$?

Accepted Answer

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

Question 3

If $$	an 	heta = \frac{4}{3}$$ and $$	heta is in $$quadrant III, what is $$\cos 	heta$$?

Accepted Answer

$$-\frac{3}{5}$$

Question 4

Which trigonometric functions are always undefined for quadrantal angles lying along the y-axis?

Accepted Answer

Tangent and secant

Question 5

Given $$\sec 	heta = 5/3$$, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{3}{5}$$

Question 6

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 7

If $$\sin 	heta = \frac{y}{r}$$ and $$r \u003e 0$$, what is the possible range of $$\sin 	heta$$?

Accepted Answer

$$[-1, 1]$$

Question 8

If $$\sin 	heta \u003e 0$$ and $$	an 	heta \u003c 0$$, in which quadrant is $$	heta$$?

Accepted Answer

Quadrant II

Question 9

Which reciprocal identity is correct?

Accepted Answer

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

Question 10

A highway grade is modeled by $$y = -0.06x in $$quadrant IV. What is the grade of the road?

Accepted Answer

$$-6\%$$

Question 11

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

Accepted Answer

No, because $$\sec 	heta$$ must be $$\leq -1 or$$ $$\geq 1$$

Question 12

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

Accepted Answer

Yes, tangent can be any real number

Question 13

Which of the following is a quotient identity?

Accepted Answer

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

Question 14

If $$	heta is in $$quadrant IV, which trigonometric functions are positive?

Accepted Answer

Cosine and secant

Question 15

Given $$\sin 	heta = -\frac{4}{5}$$ and $$	heta is in $$quadrant III, what is $$\cos 	heta$$?

Accepted Answer

$$-\frac{3}{5}$$

Question 16

If $$\sin 	heta = \frac{y}{r}$$ and $$\cos 	heta = \frac{x}{r}$$, what is $$r in $$terms of $$x$$ and $$y$$?

Accepted Answer

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

Question 17

If $$	heta is a $$quadrantal angle with terminal side along the x-axis, which functions are undefined?

Accepted Answer

Cotangent and cosecant

Question 18

If $$\sin 	heta = \frac{y}{r}$$ and $$\cos 	heta = \frac{x}{r}$$, which identity is always true?

Accepted Answer

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

Question 19

If $$	heta is in $$quadrant II, which trigonometric functions are positive?

Accepted Answer

Sine and cosecant

Trigonometric Functions and Fundamental Identities (Precalculus Study Notes)

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