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5-2 RECIPROCAL RATIOS

5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

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Page 1: 5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

5-2 RECIPROCAL RATIOS

Page 2: 5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

Remember:• Sine

• Cosine:

• Tangent:

Page 3: 5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

Basic Trig Review

x

15

178

20

y

225

x

13

Page 4: 5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

Reciprocal Trigonometric Ratios

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

Page 5: 5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

Practice:

1) If cos(x) = ¾, find sec(x)

2) If cscθ= 1.345, find sinθ

3) If tanθ = .8, find cotθ

Page 6: 5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

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

• Sin = Cos = Tan=

• Csc = sec = cot =

Page 7: 5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

Using Special Right Triangles• Remember from Geometry….

Page 8: 5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

Examples

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

5

45

45

5

30

60

Page 9: 5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

Examples

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

12

30

60

9

30

60

Page 10: 5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

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=

Page 11: 5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

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!

Page 12: 5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

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?

Page 13: 5-2 RECIPROCAL RATIOS. Remember: Sine Cosine: Tangent:

Assignment:• P. 288 (14-22) (25)