Answers LAUSD-Algebra II B Prescriptive - SummerEvaluating the Six Trigonometric Functions

Evaluating the Six Trigonometric Functions Answers

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The point P(x, y) lies on the terminal side of an angle = in standard position. What are the signs of the values of x and y?

Both x and y are positive.

Both x and y are negative.

x is positive, and y is negative.

x is negative, and y is positive.

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The point is the point at which the terminal ray of angle intersects the unit circle. What are the values for the cosine and cotangent functions for angle ?

cosine theta = Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = negative 1

cosine theta = StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = 1

cosine theta = StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = negative one-half

cosine theta = Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = one-half

The terminal side of an angle in standard position passes through P(15, –8). What is the value of ?

sine theta = fifteen-seventeenths

sine theta = negative eight-seventeenths

sine theta = eight-seventeenths

sine theta = fifteen-seventeenths

Three trigonometric functions for a given angle are shown below.What are the coordinates of point (x, y) on the terminal ray of angle , assuming that the values above were not simplified?

(–77, –36)

(–77, 36)

(–36, 77)

(36, –77)

Fatima wants to find the value of , given . Which identity would be best for Fatima to use?

cosine theta = StartFraction 1 Over secant theta EndFraction

sine squared theta + cosine squared theta = 1

Cosecant theta = StartFraction r Over y EndFraction

1 + cotangent squared theta = cosecant squared theta

Francesca drew point (–2, –10) on the terminal ray of angle , which is in standard position. She found values for the six trigonometric functions using the steps below.Step 1Step 2 Step 3Which of the following explains whether all of Francesca’s work is correct?

Each step is correct because she plotted the point, drew a line to the x-axis to form a right triangle, used the Pythagorean theorem to find the hypotenuse, and finally wrote the correct ratios for all six functions.

She made her first error in step 1 because she should have drawn the line to the y-axis to form the right triangle.

She made her first error in step 2 because she should have used a negative value for r.

She made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also results in incorrect cosecant, secant, and tangent functions.

The terminal side of an angle in standard position passes through P(–3, –4). What is the value of ?