Question

2. Given that tan 25º = a, express each of the following in terms of a.

tan 205

sin 25°

cos 65

cos 245

Answer 1

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Answer:

• tan(205°) = a
• sin(25°) = (a√(a²+1))/(a²+1)
• cos(65°) = (a√(a²+1))/(a²+1)
• cos(245°) = -(a√(a²+1))/(a²+1)

Explanation:

The tangent function is periodic with a period of 180°. So ...

tan(205°) = tan(25°) = a

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The identity relating sine and tangent is ...

sin(x) = tan(x)/√(tan²(x)+1)

Rationalizing the denominator gives ...

sin(x) = tan(x)√(tan²(x)+1)/(tan²(x)+1)

sin(25°) = a√(a²+1)/(a²+1)

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cos(65°) = sin(25°) = a√(a²+1)/(a²+1)

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cos(245°) = -sin(25°) = -a√(a²+1)/(a²+1)