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Part I- Proofs (1) We will later learn an identity that states sin(x + y) = sinxcosy + sinycosx. Use this identity to prove that sin(t + 2rn) = sin t, for any integer n and any real number t. (2) Another identity states that cos(x + y) = cosxcosy – sinxsiny. Use this identity to prove that cos(t + 2nn) = cos t, for any integer n and any real number t. Part II – Conceptual Questions (1) Explain why the tangent of an angle whose terminal side lies in the third quadrant will always have a positive value. (2) An angle, measured in radians, has its terminal side in the second quadrant. What is the complement of this angle? What is the supplement? Explain your answers.

Part I- Proofs (1) We will later learn an identity that states sin(x + y) = sinxcosy + sinycosx. Use this identity to prove that sin(t + 2rn) = sin t, for any integer n and any real number t. (2) Another identity states that cos(x + y) = cosxcosy – sinxsiny. Use this identity to prove that cos(t + 2nn) = cos t, for any integer n and any real number t. Part II – Conceptual Questions (1) Explain why the tangent of an angle whose terminal side lies in the third quadrant will always have a positive value. (2) An angle, measured in radians, has its terminal side in the second quadrant. What is the complement of this angle? What is the supplement? Explain your answers.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 21E
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Part III – Application Charleston, South Carolina (33° 47' 5" N) and Toronto, Ontario (43° 39' 4" N) lie on the same line of longitude. These lines are referred to as Great Circles of the earth. (1) Draw a diagram to depict this information. (2) Find the difference between the angles in degrees, minutes, and seconds. (3) Convert your answer from (2) to decimal degrees (round to 4 decimal places). (4) Convert your answer from (3) to radian measure (round to 4 decimal places). (5) Assuming the radius of the earth is 3960 miles, find the distance between Charleston, South Carolina and Toronto, Ontario. Give your answer to the nearest mile.
Transcribed Image Text:Part III – Application Charleston, South Carolina (33° 47' 5" N) and Toronto, Ontario (43° 39' 4" N) lie on the same line of longitude. These lines are referred to as Great Circles of the earth. (1) Draw a diagram to depict this information. (2) Find the difference between the angles in degrees, minutes, and seconds. (3) Convert your answer from (2) to decimal degrees (round to 4 decimal places). (4) Convert your answer from (3) to radian measure (round to 4 decimal places). (5) Assuming the radius of the earth is 3960 miles, find the distance between Charleston, South Carolina and Toronto, Ontario. Give your answer to the nearest mile.
Part I– Proofs (1) We will later learn an identity that states sin(x + y) = sinxcosy + sinycosx. Use this identity to prove that sin(t + 2n) = sin t, for any integer n and any real number t. (2) Another identity states that cos(x + y) = cosxcosy – sinxsiny. Use this identity to prove that cos(t + 2tn) = cos t, for any integer n and any real number t. Part II – Conceptual Questions (1) Explain why the tangent of an angle whose terminal side lies in the third quadrant will always have a positive value. (2) An angle, measured in radians, has its terminal side in the second quadrant. What is the complement of this angle? What is the supplement? Explain your answers.
Transcribed Image Text:Part I– Proofs (1) We will later learn an identity that states sin(x + y) = sinxcosy + sinycosx. Use this identity to prove that sin(t + 2n) = sin t, for any integer n and any real number t. (2) Another identity states that cos(x + y) = cosxcosy – sinxsiny. Use this identity to prove that cos(t + 2tn) = cos t, for any integer n and any real number t. Part II – Conceptual Questions (1) Explain why the tangent of an angle whose terminal side lies in the third quadrant will always have a positive value. (2) An angle, measured in radians, has its terminal side in the second quadrant. What is the complement of this angle? What is the supplement? Explain your answers.
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