Evaluating the Six Trigonometric Functions

Question 1

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

Revolt · Accepted Answer

sin(θ) =: -15/17; cos(θ) =: 8/17; tan(θ) =: -15/8; csc(θ) =: -17/15; sec(θ) =: 17/8; cot(θ) =: -8/15

Question 2

-15/8✔ -15/178/17-15

Revolt · Accepted Answer

B: -15/17

Question 3

Which value(s) are incorrect?

Revolt · Accepted Answer

A: sine (theta); C: tangent (theta); D: cosecant (theta); F: cotangent (theta)

Question 4

sine (theta) = question mark

Revolt · Accepted Answer

B: Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction

Question 5

Use the identity sin²(A) + cos²(A) = 1✔ tan²(A) + 1 = sec²(A)1 + cot²(A) = csc²(A)

Revolt · Accepted Answer

B: tan²(A) + 1 = sec²(A)

Question 6

Negative StartFraction 2 StartRoot 2 EndRoot Over 3 EndFraction

Revolt · Accepted Answer

A: Negative StartFraction 2 StartRoot 2 EndRoot Over 3 EndFraction

Question 7

Question 7

Revolt · Accepted Answer

To find the values of the six trigonometric functions for the angle θ with the terminal side passing through (5, –2), first identify the coordinates x = 5 and y = –2. Since the x-coordinate is positive and the y-coordinate is negative, the point is in Quadrant IV. Next, calculate the radius (r) using the Pythagorean theorem: r = √(5² + (–2)²) = √(25 + 4) = √29. Then apply the trigonometric definitions:
sin(θ) = y/r = –2/√29 = –2√29/29
cos(θ) = x/r = 5/√29 = 5√29/29
tan(θ) = y/x = –2/5
csc(θ) = r/y = –√29/2
sec(θ) = r/x = √29/5
cot(θ) = x/y = –5/2

Question 8

Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions. sin(θ) = cos(θ) = tan(θ) = csc(θ) = sec(θ) = cot(θ) =

Revolt · Accepted Answer

B: -15/17

Question 9

Which value(s) are incorrect?

Revolt · Accepted Answer

A: ; C: ; D: ; F:

Question 10

sine (theta) = question mark

Revolt · Accepted Answer

B:

Evaluating the Six Trigonometric Functions Answers

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