# Secondary Trig Ratios

The secondary trigonometric ratios are another useful tool in trigonometry.

Recall that, by SohCahToa, the sine of any angle in a right angled triangle is opp/hyp, the cosine of any angle is adj/hyp, and the tangent of any angle is opp/adj.

The secondary trig ratios are the reciprocal of the primary ratios.

The secondary trig ratios are:
cosecant (csc),
secant (sec)
, and cotangent (cot)

Cosecant is the reciprocal of sine. It can be written 1/sin, or simply hyp/opp.

Secant is the reciprocal of cosine. It can be written 1/cos, or simply hyp/adj.

Cotangent is the reciprocal of tangent. It can be written 1/tan, or simply adj/opp.

There are several tricks we can use to remember which trig ratios are reciprocals of each other.

Tangent and cotangent obviously match up with one another, but the other two can be tricky.

You can either remember one, or both, of the following methods:

Method 1:
Cosine and Secant go together. If you write their short forms, you get, cos and sec. If you notice, "sec" looks like the "cos" spelled backwards, except that there is an "e" instead of an "o".

Method 2:
Cos and Sec go together;
Sin and Csc go together.

The two beginning with "c" or "s" do NOT match up.

sin Ø = 6/10
sin Ø = 3/5

csc Ø = 10/6
csc Ø = 5/3

cos Ø = 8/10
cos Ø = 4/5

sec Ø = 10/8
sec Ø = 5/4

tan Ø = 6/8
tan Ø = 3/4

cot Ø = 8/6
cot Ø = 4/3

Practice Questions
Because secondary trigonometric functions are not normally explored in Grade Ten Mathematics, the text does not contain any practice questions.