Find tanθ, cscθ, and cosθ, where θ is the angle shown in the figure.

Question

Give exact values, not decimal approximations. 

tanθ =

cscθ =

cosθ =

the hypotenuse side is 13

the other side is 12

the base has no number

the θ is at the bottom between the hypotenuse and base

Answer 1

Using Pythagorean Theorem (or knowing common Pythagorean triples) we can find that the base is 5 (5, 12, 13).

Then using the definitions of the trig functions [sin = opposite/hypotenuse; cos = adjacent/hypotenuse; tan = opposite/adjacent; etc] we find:

tanΘ = 12/5

cscΘ = 13/12 (csc is the inverse of sin)

cosΘ = 5/13

Have you learned SOH CAH TOA as an easy way to remember the definitions of sine, cosine, and tangent? If so, then cosecant, secant, and cotangent are simply the inverses of those, respectively.