5-2 RECIPROCAL RATIOS

Remember:• Sine

• Cosine:

• Tangent:

Basic Trig Review

x

15

178

20

y

225

x

13

Reciprocal Trigonometric Ratios

There are actually 3 more trig ratios other than sine, cosine, and tangent. They are:

Practice:

1) If cos(x) = ¾, find sec(x)

2) If cscθ= 1.345, find sinθ

3) If tanθ = .8, find cotθ

4) Find the values of all 6 trigonometric ratios from <P(leave in radical form…no decimals!)

• Sin = Cos = Tan=

• Csc = sec = cot =

Using Special Right Triangles• Remember from Geometry….

Examples

5) Solve for the missing sides.6) Solve for the missing sides.

5

45

45

5

30

60

Examples

7) Solve for the missing sides.8) Solve for the missing sides.

12

30

60

9

30

60

Using Special Right Triangles

Use the figures to write the trig ratios for an 30°

Sin 30 = csc30 =

Cos30= sec 30=

Tan 30= cot 30=

θ Sin Cos Tan Csc Sec Cot

30

45

60

This chart is important! You need to either memorize the values, or know how to create it from scratch!

Cofunctions

Cofunctions: Two trig functions that have the same ratio.

Ex) Sin 30 = ½, and Cos 60= ½

Using the chart, name 2 other cofunctions:

What is the relationship between the angles?

Assignment:• P. 288 (14-22) (25)