Unformatted text preview: MAC1114 - Homework 2
Due Thursday, January 20
1. Show that sin(45◦ ) = cos(45◦ ) =
2. Evaluate each √ 2
2 (Hint: Draw an appropriate triangle and use the Pythagorean of the six trigonometric functions at the following values of t: (a) t = −315◦
(b) t = 32
3. In class we showed that sin(t + 2πn) = sin t and cos(t + 2πn) = cos t whenever n is an integer, and
we learned that sin t is an odd function, while cos t is an even function. Now you will derive similar
properties for the tangent function.
(a) Is tan t is an even or odd function? Why?
(b) Show that tan(t + 2πn) = tan t (Hint: use the denition of tangent in terms of sine and cosine).
(c) Although the statement in part (b) is true, the period of tan t is not 2π . Prove this by showing
that tan(t + πn) = tan t. We need to consider two cases: 1) n is even, and 2) n is odd. Case
1) was done in part (b), so here you only need to do case 2). (Hint: First, think about the unit
circle and answer this question: if sin t = a, what is sin(t + π )? If cos t = b, what is cos(t + π )?) 1 ...
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