描述
Alright, let’s look at Question 1.1. We’re told that sine theta is greater than zero, and tan theta is equal to negative two over three. So first, let’s figure out in which quadrant theta lies. Sine is positive, but tan is negative—this can only happen in the second quadrant. That’s important because it tells us the signs of all the trig ratios. Now, let’s draw a triangle in the second quadrant. Tangent is opposite over adjacent, so we take the opposite side as two, and the adjacent as negative three. Now we need the hypotenuse. We use the Pythagorean theorem: r equals the square root of two squared plus negative three squared, so that’s root of four plus nine, which is root thirteen. Now we can write the trig ratios: Sine theta is opposite over hypotenuse, so that’s two over root thirteen. Cosine theta is adjacent over hypotenuse—so that’s negative three over root thirteen. Now multiply sine theta and cosine theta: Two over root thirteen times negative three over root thirteen gives us negative six over thirteen. And that’s the final answer.