HW2 - MAC1114 Homework 2 Due Thursday January 20 1 Show...

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Unformatted text preview: MAC1114 - Homework 2 Due Thursday, January 20 1. Show that sin(45◦ ) = cos(45◦ ) = theorem). 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◦ π (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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