Find the Exact Value cos(74)

Problem

cos(74)

Solution

1. Identify the angle as 74 Since this is not a standard unit circle angle, use a sum or difference formula.

2. Rewrite the angle as a sum of two angles with known trigonometric values, such as 30 and 44 or 45 and 29 However, a more effective approach for an exact value involves the sum formula cos(A+B)=cos(A)*cos(B)−sin(A)*sin(B) using 37+37 or half-angle identities.

3. Apply the half-angle identity cos(θ)=√(,(1+cos(2*θ))/2) or recognize that 74 is 90−16

4. Use the specific exact radical form for cos(74) which is derived from the geometry of a 16−74−90 triangle or complex radical expressions.

5. Simplify the expression to its exact radical form.

Final Answer

cos(74)=(√(,50−10√(,5))−√(,6)−√(,2))/8

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