Suppose that θ is an acute angle and that tan θ = 12/18. Use a right triangle to find all the other trigonometric functions of θ.

Question

sin = ?

cos = ?

csc = ?

sec = ?

Answer 1

tanT = 12/18 = 2/3 cotT = 3/2

sinT = 2/sqr13 cscT = sqr13/2

cosT = 3/sqr13 cosT = sqr13/3

hypotenuse^2 = h = 3^2 + 2^2 = 9+4 =13

h = sqr13, sinT =2/h = 2/sqr13 cosT = 3/h = 3/sqr13

Answer 2

The tan is 2/3 which means the hypotenuse is sqrt(13).

Use the definitions to compute the trig functions.