# HW2sol - 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 ◦ ) = √ 2 2 (Hint: Draw an appropriate triangle and use the Pythagorean theorem). The key thing here is to note that since you have an isosceles triangle, the two short sides are the same. So you may have set up something like x 2 + x 2 = 1 ⇒ 2 x 2 = 1 ⇒ x 2 = 1 2 ⇒ x = q 1 2 = √ 2 2 . 2. Evaluate each of the six trigonometric functions at the following values of t : (a) t =- 315 ◦ It helps to nd a coterminal angle,- 315 ◦ + 360 ◦ = 45 ◦ . You showed in (1) that sin(45 ◦ ) = √ 2 2 and cos(45 ◦ ) = √ 2 2 , so tan(45 ◦ ) = 1 , sec(45 ◦ ) = √ 2 , csc(45 ◦ ) = √ 2 , and cot(45 ◦ ) = 1 . (b) t = 3 π 2 This is straight o the unit circle. sin 3 π 2 =- 1 , cos 3 π 2 = 0 , tan 3 π 2 = unde ned, csc 3 π 2 =- 1 , sec 3 π 2 = unde ned, cot 3 π 2 = 0 . 3. In class we showed that sin( t + 2 πn ) = sin t and cos( t + 2 πn ) = cos t whenever n is an integer, and we learned that...
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