If an angle is drawn in standard position and its terminal ray is in Quadrant III, which of the six trigonometric functions MUST have a positive value?

Question

a) None

b) Since and cosecant

c) Cosine and Secant

d) Tangent and Cotangent

Answer 1

Hi Aerin:

Here's my way of handling these quadrant questions - no memorization of reference angles needed!

Write the letters CAST, one letter per quadrant, starting in Q IV and going anti-clockwise, like this:

|

S | A

------------------------------

T | C

|

Starting ion Q IV and going anti-clockwise, we now have all the answers:

Only Cos is positive in Q IV, All are +ve in Q I, only Sin is +ve in Q II, and only Tan is +ve in Q III.

Exactly the same applies to their inverse functions: sec, cosec, and cot.

Therefore the answer to the question is (d) tan and cot.

Easy-peasy! :-)

Answer 2

In quadrant 3 only tangent and cotangent are positive

X and y are both negative so sine and cosine are negative

Tangent is y/x a negative divided by a negative is positive. Same foes for cotangent which is x/y

Answer 3

Remember: All students take Calculus

Add Sugar to Coffee

A : all trig functions are positive in Quadrant 1

S: sine is positive in quadrant 2

T: tangent is positive in quadrant 3

C: cosine is positive in quadrant 4

since the angle is in quadrant 3, the tangent (hence the cotangent) is positive