Trigonometric Ratios of 90° − θ

Move point P to observe how the point corresponding to θ moves, and how point Q corresponding to 90° − θ moves.[br]Think about how the trigonometric ratios of 90° − θ can be expressed using the trigonometric ratios of θ.[br]You can also move the slider to switch the display mode.
If the angle between the x‑axis and OP is θ, how can you express the angle of OQ measured clockwise from the y‑axis?[br]Explain your reasoning.
When θ is an acute angle, express sin(90° − θ) and cos(90° − θ) in terms of the trigonometric ratios of θ, and explain why your expressions are correct.
When θ is an acute angle, express tan(90° − θ) in terms of the trigonometric ratios of θ, and explain why your expression is correct.
When θ is an obtuse angle, what happens to sin(90° − θ), cos(90° − θ), and tan(90° − θ)?[br]Compare this with the case when θ is acute, and explain carefully, paying attention to the signs.
Kapat
– Kenichi Iijima

Bilgi: Trigonometric Ratios of 90° − θ