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Math 229 Final Exam: Trigonometry Identities - Prof. Mark D. Turner, Exams of Trigonometry

The final exam questions for a university-level mathematics course focusing on trigonometric identities. It includes questions on finding the formula for trigonometric ratios given points on a terminal side, right triangles, and special angles, as well as identifying signs of trigonometric functions in each quadrant. The document also covers reciprocal, ratio, pythagorean, negative angle, sum/difference, and double-angle identities.

Typology: Exams

Pre 2010

Uploaded on 08/17/2009

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Math 229 Final Exam: Memory Facts Name
Score
1. Given point (x, y) on the terminal side of
θ
, state the formula for r and the three trigonometric ratios
shown for
θ
in terms of x, y, and r.
r = sin
θ
= cos
θ
= tan
θ
=
2. Given right triangle ΔABC with C = 90°, state the three trigonometric ratios shown for angle A in
terms of opp, adj, and hyp.
sinA = cosA = tanA =
3. Complete the following table indicating the sign of each trigonometric function for each quadrant.
QI QII QIII QIV
sin
θ
cos
θ
tan
θ
4. First, state the radian measure of each special angle. Then give exact, simplified values for each
trigonometric function for each angle.
0° 30° 45° 60° 90° 180° 270°
Radians
sin
θ
cos
θ
tan
θ
pf2

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Math 229 Final Exam: Memory Facts Name Score

1. Given point ( x , y ) on the terminal side of θ, state the formula for r and the three trigonometric ratios

shown for θ in terms of x , y , and r.

r = sin θ = cos θ = tan θ =

  1. Given right triangleterms of opp, adj, and hyp. Δ ABC with C = 90°, state the three trigonometric ratios shown for angle A in

sin A = cos A = tan A =

  1. Complete the following table indicating the sign of each trigonometric function for each quadrant. QI QII QIII QIV

sin θ

cos θ

tan θ

  1. First, state the radian measure of each special angle. Then give exact , simplified values for each trigonometric function for each angle. 0 ° 30 ° 45 ° 60 ° 90 ° 180 ° 270 ° Radians

sin θ

cos θ

tan θ

  1. State the three reciprocal identities.

csc θ = sec θ = cot θ =

  1. State the two ratio identities.

tan θ = cot θ =

  1. State the three main Pythagorean identities.
  2. State the three negative angle identities.

sin(−θ ) = cos(−θ ) = tan(−θ ) =

  1. State the six sum/difference identities. sin( A + B ) = sin( AB ) = cos( A + B ) = cos( AB ) = tan( A + B ) = tan( AB ) =
  2. State the five double-angle identities.

sin(2 θ ) = cos(2 θ ) = tan(2 θ ) =

cos(2 θ ) =

cos(2 θ ) =

  1. State the four half-angle identities.

sin ⎛⎜⎝^ θ 2 ⎞⎟⎠ = cos ⎛⎜⎝^ θ 2 ⎞⎟⎠ = tan ⎛⎜⎝^ θ 2 ⎞⎟⎠ =

tan ⎛⎜⎝^ θ 2 ⎞⎟⎠ =