Answers JPS-202526SS-Evergreen HS-Algebra II B-CR-NobleThe Unit Circle

Evaluating the Six Trigonometric Functions Answers

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Given that , what is the value of , for ?

Negative StartRoot StartFraction 20 Over 29 EndFraction EndRoot

Negative StartFraction 20 Over 29 EndFraction

StartFraction 20 Over 29 EndFraction

StartRoot StartFraction 20 Over 29 EndFraction EndRoot

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Based on Pythagorean identities, which equation is true?

sine squared theta minus 1 = cosine squared theta

secant squared theta minus tangent squared theta = negative 1

negative cosine squared theta minus 1 = negative sine squared theta

cotangent squared theta minus cosecant squared theta = negative 1

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

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.

Which Pythagorean identity is correct?

sine squared (theta) + 1 = cosecant squared (theta)

tangent squared (theta) + 1 = secant squared (theta)

1 minus cotangent squared (theta) = cosecant squared (theta)

1 minus cosine squared (theta) = tangent squared (theta)

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

tangent theta = Negative four-thirds

tangent theta = Negative three-fourths

Tangent theta = three-fourths

Tangent theta = four-thirds

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?