## EXPLORATION 1 Exploring Trigonometric Functions There are twice as many…
MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions
Problem
## EXPLORATION 1 Exploring Trigonometric Functions
There are twice as many trigonometric functions as there are triangle sides that define them, so we can already explore some ways in which the trigonometric functions relate to each other. Doing this Exploration will help you learn which ratios are which.
(1) Each of the six trig functions can be paired to another that is its reciprocal. Find the three pairs of reciprocals.
(2) Which trig function can be written as the quotient sinθ/cosθ ?
(3) Which trig function can be written as the quotient cscθ/cotθ ?
(4) What is the (simplified) product of all six trig functions multiplied together?
(5) Which two trig functions must be less than 1 for any acute angle θ ? [Hint: What is always the longest side of a right triangle?]