find tan B and CSC B if sec B = 3/2 and tan B < 0

Question

Use the Pythagorean identities to find each function value.

Answer 1

tanB = - √(sec²B - 1) √= - √((3/2)² - 1) = - √(9/4 - 1) = - √5/2; cosB = 1/secB = 1/(3/2) = 2/3;

cotB = 1/tanB = - 2/√5; then cscB = cotB/(cosB) = (-2/√5)/(2/3) = - 3/√5