[b]Goal:[/b][br]Demonstrate why trigonometric function names change when using the vertical Y-axis (90°) as a reference.[br][br][b]Description:[/b][br]When we measure an angle from the vertical Y-axis, the triangle "tips over." The side that was "Opposite" to the angle becomes "Adjacent" to the complementary angle. This geometric swap is why Sine (Opposite) becomes Cosine (Adjacent).[br][br][b]Instructions:[br][br][/b]1. Set the slider to an angle between 0° and 180° (e.g., 50°).[br]The gray angle shows how far your angle is from the 90° line.[br]Notice how the applet rewrites the angle as (90° - + x).[br][br]2. Look at the right triangle formed by this gray angle near the 90° reference axis.[br][list][*]Examine the sides of this small triangle.[/*][*]Which side is opposite to the gray angle?[/*][*]Which side is adjacent to the gray angle?[/*][*]How do these compare to the opposite and adjacent sides of the original large-angle triangle?[/*][/list][br]3. Use your observations to decide which function value (sin or cos) the small triangle’s sides now represent.[br][br]4. Check the equations on the right to confirm the name and sign changes.[br][br][br][br]
[i][color=#999999][size=150]Write your answers in the given space below each question.[/size][/color][/i]
1) For every complementary angles a and b, such that a + b = 90⁰[br] sin(a) = cos(b)
2) For 0° < x < 90°,[br] cot(90° + x) = cot(x)[br]
3) For 0° < α < 90°,[br] cos(90° + α) = –sin(α)
4) cot(48°) = tan(x)[br] x = ?
5) cot(110°) = – tan(x)[br] x = ?
6) cos(62°) = sin(x)[br] x = ?
(Be careful!)[br][br]7) sin(50°) = – sin(x) [br] x = ?