During a trigonometry lesson a group of students wrote down some statements about what they expected to happen when they looked at the values of trigonometric functions of some angles - Junior Cycle Mathematics - Question 15 - 2014

Yes, the statement (ii) is correct. The sine function demonstrates this as sin(90°) = 1, but sin(180°) results in -1.

No, the statement (iii) is incorrect. A practical example is with cosine: cos(45°) = 0.7071, but cos(90°) = 0, indicating a decrease, not always an increase.

To find sin(60°) in an equilateral triangle, we can bisect the triangle to form two right-angled triangles. Let the side length be 2 cm.

Using Pythagorean Theorem:

1. The vertical height will be represented by x:

   $1 + x^2 = 2^2$

   $$$$

ightarrow x = \sqrt{3}$$

2. Now, using the definition of sine in a right-angled triangle:

   $sin(60°) = \frac{Opposite}{Hypotenuse} \rightarrow sin(60°) = \frac{\sqrt{3}}{2}$