Math Problem Statement
Find the exact value of the expression.
cosine left parenthesis 60 degrees plus 225 degrees right parenthesiscos(60°+225°)
Question content area bottom
Part 1
Apply the sum and difference identities. Choose the correct answer below.
A.cosine 60 degrees cosine 225 degrees plus sine 60 degrees sine 225 degrees
cosine 60 degrees cosine 225 degreescos60°cos225°plus+sine 60 degrees sine 225 degreessin60°sin225°
B.sine 60 degrees cosine 225 degrees minus cosine 60 degrees sine 225 degrees
sine 60 degrees cosine 225 degreessin60°cos225°minus−cosine 60 degrees sine 225 degreescos60°sin225°
C.StartFraction tangent 60 degrees minus tangent 225 degrees Over 1 plus tangent 60 degrees tangent 225 degrees EndFraction
StartFraction tangent 60 degrees minus tangent 225 degrees Over 1 plus tangent 60 degrees tangent 225 degrees EndFractiontan60°−tan225°1+tan60°tan225°
D.sine 60 degrees cosine 225 degrees plus cosine 60 degrees sine 225 degrees
sine 60 degrees cosine 225 degreessin60°cos225°plus+cosine 60 degrees sine 225 degreescos60°sin225°
E.cosine 225 degrees cosine 225 degrees plus sine 60 degrees sine 60 degrees
cosine 225 degrees cosine 225 degreescos225°cos225°plus+sine 60 degrees sine 60 degreessin60°sin60°
F.cosine 60 degrees cosine 60 degrees minus sine 225 degrees sine 225 degrees
cosine 60 degrees cosine 60 degreescos60°cos60°minus−sine 225 degrees sine 225 degreessin225°sin225°
G.cosine 60 degrees cosine 60 degrees plus sine 225 degrees sine 225 degrees
cosine 60 degrees cosine 60 degreescos60°cos60°plus+sine 225 degrees sine 225 degreessin225°sin225°
H.sine 60 degrees cosine 60 degrees minus cosine 225 degrees sine 225 degrees
sine 60 degrees cosine 60 degreessin60°cos60°minus−cosine 225 degrees sine 225 degreescos225°sin225°
I.StartFraction tangent 225 degrees minus tangent 60 degrees Over 1 minus tangent 60 degrees tangent 225 degrees EndFraction
StartFraction tangent 225 degrees minus tangent 60 degrees Over 1 minus tangent 60 degrees tangent 225 degrees EndFractiontan225°−tan60°1−tan60°tan225°
J.sine 60 degrees cosine 60 degrees plus cosine 225 degrees sine 225 degrees
sine 60 degrees cosine 60 degreessin60°cos60°plus+cosine 225 degrees sine 225 degreescos225°sin225°
K.sine 225 degrees cosine 225 degrees minus sine 60 degrees cosine 60 degrees
sine 225 degrees cosine 225 degreessin225°cos225°minus−sine 60 degrees cosine 60 degreessin60°cos60°
L.cosine 225 degrees cosine 225 degrees minus sine 60 degrees sine 60 degrees
cosine 225 degrees cosine 225 degreescos225°cos225°minus−sine 60 degrees sine 60 degreessin60°sin60°
M.StartFraction tangent 60 degrees plus tangent 225 degrees Over 1 minus tangent 60 degrees tangent 225 degrees EndFraction
StartFraction tangent 60 degrees plus tangent 225 degrees Over 1 minus tangent 60 degrees tangent 225 degrees EndFractiontan60°+tan225°1−tan60°tan225°
N.cosine 60 degrees cosine 225 degrees minus sine 60 degrees sine 225 degrees
cosine 60 degrees cosine 225 degreescos60°cos225°
Solution
The given problem involves applying the sum identity for cosine to compute . The sum identity for cosine is:
Here, and . Using the formula:
Correct Answer:
The correct option is: N.
Would you like to evaluate this further and find the exact value, or review related concepts?
5 Related Questions:
- What are the exact values of , , , and ?
- How does the cosine identity differ from the sine identity for sums?
- What quadrant does the angle (i.e., ) lie in, and what does that imply about its cosine?
- Can the sum identity for cosine be applied to angles in radians?
- How would you derive the tangent sum identity starting from sine and cosine sum identities?
Tip:
For trigonometric problems, always simplify using identities and verify the quadrant to determine the sign of the trigonometric functions.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Cosine Function
Sum of Angles Identity
Formulas
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
Theorems
Sum Identity for Cosine
Suitable Grade Level
Grades 9-12