Trigonometric Sum Identities — Quiz

Question 1

What is the exact value of sine of open paren v plus w close paren , given sine v is equal to negative 3 fifths , cosine w is equal to 10 over 11 , v is an angle in Quadrant III, and w is an angle is Quadrant IV?

Revolt · Accepted Answer

the fraction with numerator negative 30 plus 4 square root of 21 and denominator 55

Question 2

What is the exact value of sine of open paren 345 degrees close paren ?

Revolt · Accepted Answer

the fraction with numerator negative square root of 6 plus square root of 2 and denominator 4

Question 3

If tangent m is equal to 1 half and tangent n is equal to negative 6 , what is the exact value of tangent of open paren m plus n close paren ?

Revolt · Accepted Answer

negative 11 eighths

Question 4

Which set of steps can be used to prove the sine sum identity, sine of open paren x plus y close paren is equal to sine x plus cosine x ?

Revolt · Accepted Answer

Use the supplementary relationship between sine and cosine to rewrite sine of open paren x plus y close paren as cosine of open paren pi over 2 minus open paren x plus y close paren close paren . Apply the cosine sum identity. Then simplify using sine of negative y is equal to negative sine times y and cosine of negative y is equal to cosine of y .

Question 5

Which steps can be used to verify that tangent of open paren w plus pi close paren is equal to tangent of w ?

Revolt · Accepted Answer

Rewrite tangent of open paren w plus pi close paren using the tangent sum identity. Then simplify the resulting expression using tangent of pi is equal to 0 .

Question 6

What is the exact value of cosine of open paren 195 degrees close paren ?

Revolt · Accepted Answer

the fraction with numerator negative square root of 6 plus square root of 2 and denominator 4

Question 7

Solve: sine of open paren 11 pi over 2 plus x close paren is equal to negative 1 half for left bracket pi comma 2 pi right bracket

Revolt · Accepted Answer

5 pi over 3

Question 8

Which expression is equivalent to sine open paren 84 degrees close paren plus cosine open paren 84 degrees close paren ?

Revolt · Accepted Answer

sine of open paren 127 degrees close paren; cosine of open paren 127 degrees close paren

Question 9

What is the exact value of cosine open paren 11 pi over 21 close paren minus sine open paren 11 pi over 21 close paren ?

Revolt · Accepted Answer

negative 1 half

Question 10

Which expression is equivalent to cosine of open paren pi over 2 plus r close paren for all values of r ?

Revolt · Accepted Answer

negative sine times r

Trigonometric Sum Identities — Quiz Answers

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