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Evaluating the Six Trigonometric Functions Answers

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

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

-1

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Solving the identity, tan(A) = _____.

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What is cot(A)?

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Which value(s) are incorrect?

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

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

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to find the value of (A).

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tan

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Which did you include in your response?

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Plot the point (5, –2) and draw a line from the point to the x-axis to make a right triangle.
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Use the Pythagorean theorem to find the length of the hypotenuse.
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Use the definition of each trigonometric function to find the values.
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Determine the appropriate sign for each function, using the fact that the terminal side is in Quadrant IV.

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